{"id":1927,"date":"2022-11-04T08:29:11","date_gmt":"2022-11-04T08:29:11","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=1927"},"modified":"2022-11-04T08:29:11","modified_gmt":"2022-11-04T08:29:11","slug":"ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-3\/","title":{"rendered":"NCERT Solutions Class 7 Maths Chapter 6 The Triangle and its Properties Ex 6.3"},"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; 6 (The Triangle and its Properties)<\/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; 6 The Triangle and its Properties <\/strong>Exercise 6.3 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Chapter : 6 The Triangles and its Properties<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-1\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.1<\/span><\/a><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-2\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.2<\/span><\/a><\/span><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-4\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.4<\/span><\/a><\/span><\/span><\/li>\n<li><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-6-the-triangle-and-its-properties-ex-6-5\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 6.5<\/span><\/a><\/span><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 6.3\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. Find the value of the unknown x in the following diagrams:<br \/>\n<\/strong><strong>(i) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1964\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"216\" height=\"153\" \/>\u00a0 (ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1965\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1ii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"223\" height=\"134\" \/>\u00a0 \u00a0(iii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1966\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1iii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"218\" height=\"214\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1967\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1iv.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"183\" height=\"170\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (v) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1968\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1v.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"189\" height=\"161\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0(vi) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1969\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q1vi.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"188\" height=\"111\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(i)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + 50\u00b0 + 60\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 110\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x = 180\u00b0 \u2013 110\u00b0 = 70\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + 90\u00b0 + 30 = 180\u00b0 [\u2206 is right angled triangle]<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 120\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x \u2013 180\u00b0 \u2013 120\u00b0 = 60\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iii)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + 30\u00b0 + 110\u00b0 \u2013 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 140\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x = 180\u00b0 \u2013 140\u00b0 = 40\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iv)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220x + 50\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2x + 50\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2x = 180\u00b0 \u2013 50\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2x = 130\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{130^{\\circ}}{2}\" alt=\"\\frac{130^{\\circ}}{2}\" align=\"absmiddle\" \/>= <span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-13\" class=\"msubsup\"><span id=\"MathJax-Span-14\" class=\"mn\">65<\/span><span id=\"MathJax-Span-15\" class=\"texatom\"><span id=\"MathJax-Span-16\" class=\"mrow\"><span id=\"MathJax-Span-17\" class=\"mo\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(v)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220x +\u2220x =180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 3\u2220x = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234\u00a0<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-18\" class=\"math\"><span id=\"MathJax-Span-19\" class=\"mrow\"><span id=\"MathJax-Span-20\" class=\"mi\">\u2220<\/span><span id=\"MathJax-Span-21\" class=\"mi\">x <\/span><span id=\"MathJax-Span-22\" class=\"mo\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{180^{\\circ}}{3}\" alt=\"\\frac{180^{\\circ}}{3}\" align=\"absmiddle\" \/> <\/span><span id=\"MathJax-Span-30\" class=\"mo\">= <\/span><span id=\"MathJax-Span-31\" class=\"msubsup\"><span id=\"MathJax-Span-32\" class=\"mn\">60<\/span><span id=\"MathJax-Span-33\" class=\"texatom\"><span id=\"MathJax-Span-34\" class=\"mrow\"><span id=\"MathJax-Span-35\" class=\"mo\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(vi)<\/strong> By angle sum property of a triangle, we have<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">x + 2 x + 90\u00b0 = 180\u00b0 (\u2206 is right angled triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 3x + 90\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 3x = 180\u00b0 \u2013 90\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 3x = 90\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234\u00a0<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-36\" class=\"math\"><span id=\"MathJax-Span-37\" class=\"mrow\"><span id=\"MathJax-Span-38\" class=\"mi\">x <\/span><span id=\"MathJax-Span-39\" class=\"mo\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{90^{\\circ}}{3}\" alt=\"\\frac{90^{\\circ}}{3}\" align=\"absmiddle\" \/> <\/span><span id=\"MathJax-Span-47\" class=\"mo\">=<\/span><span id=\"MathJax-Span-48\" class=\"msubsup\"><span id=\"MathJax-Span-49\" class=\"mn\">30<\/span><span id=\"MathJax-Span-50\" class=\"texatom\"><span id=\"MathJax-Span-51\" class=\"mrow\"><span id=\"MathJax-Span-52\" class=\"mo\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Find the values of the unknowns x and y in the following diagrams:<\/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 size-full wp-image-1970\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2i.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"195\" height=\"98\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(ii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1971\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2ii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"159\" height=\"148\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(iii) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1972\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2iii.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"186\" height=\"143\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1973\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2iv.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"246\" height=\"125\" \/>(v) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1974\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2v.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"193\" height=\"154\" \/>\u00a0 \u00a0 \u00a0(vi) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1975\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-6.3-Q2vi.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"193\" height=\"176\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(i)<\/strong> \u2220x + 50\u00b0 = 120\u00b0 (Exterior angle of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x = 120\u00b0- 50\u00b0 = 70\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220y + 50\u00b0 = 180\u00b0 (Angle sum property of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">70\u00b0 + \u2220y + 50\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220y + 120\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220y = 180\u00b0 \u2013 120\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220y = 60\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Thus \u2220x = 70 and \u2220y \u2013 60\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii)<\/strong> \u2220y = 80\u00b0 (Vertically opposite angles are same)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220y + 50\u00b0 = 180\u00b0 (Angle sum property of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 80\u00b0 + 50\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 130\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x = 180\u00b0 \u2013 130\u00b0 = 50\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Thus, \u2220x = 50\u00b0 and \u2220y = 80\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iii)<\/strong> \u2220y + 50\u00b0 + 60\u00b0 = 180\u00b0 (Angle sum property of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220y + 110\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220y = 180\u00b0- 110\u00b0 = 70\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220y = 180\u00b0 (Linear pairs)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220x + 70\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 \u2220x = 180\u00b0 \u2013 70\u00b0 = 110\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Thus, \u2220x = 110\u00b0 and y = 70\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iv)<\/strong> \u2220x = 60\u00b0 (Vertically opposite angles)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220y + 30\u00b0 = 180\u00b0 (Angle sum property of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 60\u00b0 + \u2220y + 30\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220y + 90\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 \u2220y = 180\u00b0 \u2013 90\u00b0 = 90\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Thus, \u2220x = 60\u00b0 and \u2220y = 90\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(v)<\/strong> \u2220y = 90\u00b0 (Vertically opposite angles)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2220x + \u2220x + \u2220y = 180\u00b0 (Angle sum property of a triangle)<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2 \u2220x + 90\u00b0 = 180\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2\u2220x = 180\u00b0 \u2013 90\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 2\u2220x = 90\u00b0<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234\u00a0<span id=\"MathJax-Element-4-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-53\" class=\"math\"><span id=\"MathJax-Span-54\" class=\"mrow\"><span id=\"MathJax-Span-55\" class=\"mi\">\u2220<\/span><span id=\"MathJax-Span-56\" class=\"mi\">x <\/span><span id=\"MathJax-Span-57\" class=\"mo\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{90^{\\circ}}{2}\" alt=\"\\frac{90^{\\circ}}{2}\" align=\"absmiddle\" \/> <\/span><span id=\"MathJax-Span-65\" class=\"mo\">= <\/span><span id=\"MathJax-Span-66\" class=\"msubsup\"><span id=\"MathJax-Span-67\" class=\"mn\">45<\/span><span id=\"MathJax-Span-68\" class=\"texatom\"><span id=\"MathJax-Span-69\" class=\"mrow\"><span id=\"MathJax-Span-70\" class=\"mo\">\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Thus, \u2220x = 45\u00b0 and \u2220y = 90\u00b0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(vi) <\/strong>From the rule of vertically opposite angles,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 x = y<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">Then, We know that,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">The sum of all the interior angles of a triangle is 180<sup>o<\/sup>.<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u21d2 x + x + x = 180<sup>o<br \/>\n<\/sup>\u21d2 3x = 180<sup>o<br \/>\n<\/sup>\u21d2 x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{180^{\\circ}}{3}\" alt=\"\\frac{180^{\\circ}}{3}\" align=\"absmiddle\" \/> = 60<sup>o<\/sup><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 7 Mathematics\u00a0 Chapter &#8211; 6 (The Triangle and its Properties) The NCERT Solutions in English Language for Class 7 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