{"id":1891,"date":"2022-11-03T12:42:55","date_gmt":"2022-11-03T12:42:55","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=1891"},"modified":"2022-11-03T12:42:55","modified_gmt":"2022-11-03T12:42:55","slug":"ncert-solutions-class-7-maths-chapter-5-lines-and-angles-ex-5-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-5-lines-and-angles-ex-5-1\/","title":{"rendered":"NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 7 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 5 (Lines and Angles)<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 7 Mathematics <strong>Chapter &#8211; 5 Lines and Angles <\/strong>Exercise 5.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\"><strong style=\"color: #000000;\">Chapter : 5 Lines and Angles<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-5-lines-and-angles-ex-5-2\" target=\"_blank\" rel=\"noopener\"><span style=\"color: #0000ff; font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 5.2<\/span><\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 5.1\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>1. Find the complement of each of the following angles:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1896 size-full\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q1i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"131\" height=\"54\" \/>(ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1897\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q1ii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"140\" height=\"106\" \/> (iii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1898\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q1iii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"129\" height=\"117\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> Two angles are said to be complementary if the sum of their measures is 90<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 20<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its complement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 20<sup>o<\/sup>\u00a0= 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 90<sup>o<\/sup>\u00a0\u2013 20<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 70<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the complement of the given angle measures 70<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><b>(ii) <\/b>Two angles are said to be complementary if the sum of their measures is 90<\/span><sup style=\"font-family: georgia, palatino, serif;\">o<\/sup><span style=\"font-family: georgia, palatino, serif;\">.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 63<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its complement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 63<sup>o<\/sup>\u00a0= 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 90<sup>o<\/sup>\u00a0\u2013 63<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 27<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the complement of the given angle measures 27<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><b>(iii)<br \/>\n<\/b>Two angles are said to be complementary if the sum of their measures is 90<\/span><sup style=\"font-family: georgia, palatino, serif;\">o<\/sup><span style=\"font-family: georgia, palatino, serif;\">.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 57<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its complement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 57<sup>o<\/sup>\u00a0= 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">= x = 90<sup>o<\/sup>\u00a0\u2013 57<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 33<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the complement of the given angle measures 33<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>2. Find the supplement of each of the following angles:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1899\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q2i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"187\" height=\"107\" \/>(ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1900\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q2ii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"175\" height=\"102\" \/>(iii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1901\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q2iii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"228\" height=\"37\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> Two angles are said to be supplementary if the sum of their measures is 180<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 105<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its supplement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 105<sup>o<\/sup>\u00a0= 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 180<sup>o<\/sup>\u00a0\u2013 105<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 75<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the supplement of the given angle measures 75<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Two angles are said to be supplementary if the sum of their measures is 180<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 87<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its supplement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 87<sup>o<\/sup>\u00a0= 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 180<sup>o<\/sup>\u00a0\u2013 87<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 93<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the supplement of the given angle measures 93<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Two angles are said to be supplementary if the sum of their measures is 180<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">The given angle is 154<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of its supplement be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + 154<sup>o<\/sup>\u00a0= 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 180<sup>o<\/sup>\u00a0\u2013 154<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 26<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the supplement of the given angle measures 93<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>3. Identify which of the following pairs of angles are complementary and which are supplementary.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) 65<sup>o<\/sup>, 115<sup>o<br \/>\n<\/sup><\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) 63\u00b0, 27\u00b0<br \/>\n(iii) 112\u00b0, 68\u00b0<br \/>\n(iv) 130\u00b0, 50\u00b0<br \/>\n(v) 45\u00b0, 45\u00b0<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) 65<sup>o<\/sup>, 115<sup>o<\/sup><\/strong><br \/>\n65\u00b0 (+) 115\u00b0 = 180\u00b0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 These angles are <strong>supplementary angles<\/strong>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) 63<sup>o<\/sup>, 27<sup>o<br \/>\n<\/sup><\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">63\u00b0 (+) 27\u00b0 = 90\u00b0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 These angles are <strong>complementary angles<\/strong>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) 112<sup>o<\/sup>, 68<sup>o<br \/>\n<\/sup><\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">112\u00b0 (+) 68\u00b0 = 180\u00b0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 These angles are <strong>supplementary angles<\/strong>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv) 130<sup>o<\/sup>, 50<sup>o<br \/>\n<\/sup><\/strong><\/span>130\u00b0 (+) 50\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 These angles are supplementary angles.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(v) 45<sup>o<\/sup>, 45<sup>o<br \/>\n<\/sup><\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">45\u00b0 (+) 45\u00b0 = 90\u00b0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 These angles are <strong>complementary angles<\/strong>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(vi) 80<sup>o<\/sup>, 10<sup>o<br \/>\n<\/sup><\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">80\u00b0 (+) 10\u00b0 = 90\u00b0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 These angles are <strong>complementary angles<\/strong>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. Find the angles which is equal to its complement.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the required angle be x\u00b0.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">We know that, sum of measures of complementary angle pair is 90<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + x = 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 2x = 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{90}{2}\" alt=\"\\frac{90}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 45<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the required angle measures is 45<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. Find the angles which is equal to its supplement.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Let the measure of the required angle be x<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">We know that, sum of measures of supplementary angle pair is 180<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + x = 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 2x = 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{180}{2}\" alt=\"\\frac{180}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x = 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, the required angle measures is 90<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>6. In the given figure, \u22201 and \u22202 are supplementary angles. If \u22201 is decreased, what changes should take place in \u22202 so that both angles still remain supplementary.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1902\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q6.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"268\" height=\"119\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">From the question, it is given that,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u22201 and \u22202 are supplementary angles.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">If \u22201 is decreased, then \u22202 must be increased by the same value.<br \/>\nHence, this angle pair remains supplementary.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>7. Can two angles be supplementary if both of them are:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Acute?<br \/>\n(ii) Obtuse?<br \/>\n(iii) Right?<br \/>\n<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Acute?<\/strong><br \/>\nNo. If two angles are acute, means less than 90<sup>o<\/sup>, the two angles cannot be supplementary. Because, their sum will be always less than 90<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) Obtuse?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">No. If two angles are obtuse, means more than 90<sup>o<\/sup>, the two angles cannot be supplementary. Because, their sum will be always more than 180<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) Right?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Yes. If two angles are right, means both measures 90<sup>o<\/sup>, then two angles can form a supplementary pair.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 90<sup>o\u00a0<\/sup>+ 90<sup>o<\/sup>\u00a0= 180<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. An angle is greater than 45<sup>o<\/sup>. Is its complementary angle greater than 45<sup>o<\/sup>\u00a0or equal to 45<sup>o<\/sup>\u00a0or less than 45<sup>o<\/sup>?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Let us assume the complementary angles be x and y,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">We know that, sum of measures of complementary angle pair is 90<sup>o<\/sup>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Then,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + y = 90<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">It is given in the question that p &gt; 45<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Adding q on both the sides,<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 x + y &gt; 45<sup>o\u00a0<\/sup>+ y<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 90<sup>o<\/sup>\u00a0&gt; 45<sup>o\u00a0<\/sup>+ y<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 90<sup>o<\/sup>\u00a0\u2013 45<sup>o<\/sup> &gt; y<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 y &lt; 45<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Hence, its complementary angle is less than 45<sup>o<\/sup>.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>9. In the adjoining figure:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1903\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q9.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"271\" height=\"219\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) Is \u22201 adjacent to \u22202?<br \/>\n(ii) Is \u2220AOC adjacent to\u2220AOE?<br \/>\n(iii) Do \u2220COE and \u2220EOD form a linear pair?<br \/>\n(iv) Are \u2220BOD and \u2220DOA supplementary?<br \/>\n(v) Is \u22201 vertically opposite angle to \u22204?<br \/>\n(vi) What is the vertically opposite angle of \u22205?<br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n(i) Is \u22201 adjacent to \u22202?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Yes, \u22201 and \u22202 are adjacent angles.<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) Is \u2220AOC adjacent to \u2220AOE?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">No, \u2220AOC is not adjacent to \u2220AOE. [ \u2235\u00a0 OC and OE do not lie on either side of common arm OA] .<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) Do \u2220COE and \u2220EOD form a linear pair?<br \/>\n<\/strong>Yes, \u2220COE and \u2220EOD form a linear pair of angles.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv) Are \u2220BOD and \u2220DOA supplementary?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Yes, \u2220BOD and \u2220DOA are supplementary. [\u2235 \u2220BOD + \u2220DOA = 180\u00b0]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(v) Is \u22201 vertically opposite to \u22204?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Yes, \u22201 is vertically opposite to \u22204.<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(vi) What is the vertically opposite angle of \u22205?<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Vertically opposite angle of \u22205 is \u22202 + \u22203 i.e. \u2220BOC.<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>10. Indicate which pairs of angles are:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Vertically opposite angles.<br \/>\n(ii) Linear pairs.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1904\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q10.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"304\" height=\"213\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q10.png 304w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q10-300x210.png 300w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Vertically opposite angles.<\/strong><br \/>\nVertically opposite angles are \u22201 and \u22204, \u22205 and (\u22202 + \u22203)<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) Linear pairs.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u22201 and \u22205, \u22205 and \u22204<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>11. In the following figure, is \u22201 adjacent to \u22202? Give reasons.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1905\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q11.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"253\" height=\"156\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u22201 and \u22202 are not adjacent angles. Because, they are not lie on the same vertex.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>12. Find the values of the angles x, y, and z in each of the following:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1907\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q12.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"253\" height=\"137\" \/> (ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1906\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q12ii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"255\" height=\"160\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q12ii.png 312w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q12ii-300x188.png 300w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n(i)<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220x = 55<sup>o<\/sup>, because vertically opposite angles.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220x + \u2220y = 180<sup>o<\/sup>\u00a0 \u00a0&#8212;&#8212;-[\u2235 linear pair]<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 55<sup>o<\/sup>\u00a0+ \u2220y = 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220y = 180<sup>o<\/sup>\u00a0\u2013 55<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220y = 125<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Then, \u2220y = \u2220z\u00a0 &#8212;&#8212;&#8212; [\u2235 vertically opposite angles]<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 \u2220z = 125<sup>o<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220z = 40<sup>o<\/sup>, because vertically opposite angles.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220y + \u2220z = 180<sup>o<\/sup>\u00a0 \u00a0 &#8212;&#8212;&#8212;&#8212;&#8211; [\u2235 linear pair]<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220y + 40<sup>o<\/sup>\u00a0= 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220y = 180<sup>o<\/sup>\u00a0\u2013 40<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220y = 140<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">Then, 40 + \u2220x + 25 = 180<sup>o<\/sup>\u00a0 &#8212;&#8212;&#8212;&#8212; [\u2235angles on straight line]<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 65 + \u2220x = 180<sup>o<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">\u21d2 \u2220x = 180<sup>o<\/sup>\u00a0\u2013 65<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2234 \u2220x = 115<sup>o<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>13. Fill in the blanks:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) If two angles are complementary, then the sum of their measures is ________.<br \/>\n(ii) If two angles are supplementary, then the sum of their measures is ________.<br \/>\n(iii) Two angles forming a linear pair are ________.<br \/>\n(iv) If two adjacent angles are supplementary, they form a ________.<br \/>\n(v) If two lines intersect at a point, then the vertically opposite angles are always ________.<br \/>\n(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are ________.<br \/>\n<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">(i) If two angles are complementary, then the sum of their measures is <span style=\"text-decoration: underline;\"><strong>90<sup>o<\/sup><\/strong><\/span>.<br \/>\n(ii) If two angles are supplementary, then the sum of their measures is <span style=\"text-decoration: underline;\"><strong>180<sup>o<\/sup><\/strong><\/span>.<br \/>\n(iii) Two angles forming a linear pair are <span style=\"text-decoration: underline;\"><strong>Supplementary<\/strong><\/span>.<br \/>\n(iv) If two adjacent angles are supplementary, they form a <span style=\"text-decoration: underline;\"><strong>Linear pair<\/strong><\/span>.<br \/>\n(v) If two lines intersect at a point, then the vertically opposite angles are always <span style=\"text-decoration: underline;\"><strong>Equal<\/strong><\/span>.<br \/>\n(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are <span style=\"text-decoration: underline;\"><strong>Obtuse angle<\/strong><\/span>.<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>14. In the adjoining figure, name the following pairs of angles.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1908\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-5.1-Q14.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"286\" height=\"121\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) Obtuse vertically opposite angles.<br \/>\n(ii) Adjacent complementary angles.<br \/>\n(iii) Equal supplementary angles.<br \/>\n(iv) Unequal supplementary angles.<br \/>\n(v) Adjacent angles but do not form a linear pair.<br \/>\n<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n(i) Obtuse vertically opposite angles<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220AOD and \u2220BOC are obtuse vertically opposite angles in the given figure.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) Adjacent complementary angles<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220EOA and \u2220AOB are adjacent complementary angles in the given figure.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) Equal supplementary angles<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220EOB and EOD are the equal supplementary angles in the given figure.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv) Unequal supplementary angles<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220EOA and \u2220EOC are the unequal supplementary angles in the given figure.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(v) Adjacent angles that do not form a linear pair<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">\u2220AOB and \u2220AOE, \u2220AOE and \u2220EOD, \u2220EOD and \u2220COD are the adjacent angles that do not form a linear pair in the given figure.<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 7 Mathematics\u00a0 Chapter &#8211; 5 (Lines and Angles) The NCERT Solutions in English Language for Class 7 Mathematics Chapter &#8211; 5 Lines and Angles Exercise 5.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 5 Lines and Angles NCERT Solution Class 7 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[219],"tags":[290,291,283,5],"class_list":["post-1891","post","type-post","status-publish","format-standard","hentry","category-class-7-maths","tag-ncert-class-7-maths-chapter-5-simple-equations-in-english","tag-ncert-solutions-class-7-maths-chapter-5-in-english","tag-ncert-solutions-class-7-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - 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