NCERT Solutions Class 8 Mathematics
Chapter – 3 (Understanding Quadrilaterals)
The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 3 Understanding Quadrilaterals Exercise 3.2 has been provided here to help the students in solving the questions from this exercise.
Chapter 3: Understanding Quadrilaterals
- NCERT Solution Class 8 Maths Ex – 3.1
- NCERT Solution Class 8 Maths Ex – 3.3
- NCERT Solution Class 8 Maths Ex – 3.4
Exercise – 3.2
1. Find x in the following figures.
Solution –
(a)
125° + m = 180° ⇒ m = 180° – 125° = 55° (Linear pair)
125° + n = 180° ⇒ n = 180° – 125° = 55° (Linear pair)
x = m + n (The exterior angle of a triangle is equal to the sum of the two opposite interior angles)
⇒ x = 55° + 55° = 110°
(b)
Two interior angles are right angles = 90°
70° + m = 180° ⇒ m = 180° – 70° = 110° (Linear pair)
60° + n = 180° ⇒ n = 180° – 60° = 120° (Linear pair) The figure is having five sides and is a pentagon.
Thus, sum of the angles of a pentagon = 540°
⇒ 90° + 90° + 110° + 120° + y = 540°
⇒ 410° + y = 540° ⇒ y = 540° – 410° = 130°
x + y = 180° (Linear pair)
⇒ x + 130° = 180°
⇒ x = 180° – 130° = 50°
2. Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Solution –
(i) Each exterior angle = Sum of exterior angles/Number of angles = = 40°
(ii) Each exterior angle = sum of exterior angles/Number of angles = = 24°
3. How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution – Each exterior angle = sum of exterior angles/Number of angles
24° = 360/ Number of sides
⇒ Number of sides = = 15
Thus, the regular polygon has 15 sides.
4. How many sides does a regular polygon have if each of its interior angles is 165°?
Solution –
Interior angle = 165°
Exterior angle = 180° – 165° = 15°
Number of sides = sum of exterior angles/exterior angles
⇒ Number of sides = = 24°
Thus, the regular polygon has 24 sides.
5.
(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Solution –
(a) Exterior angle = 22°
Number of sides = sum of exterior angles/ exterior angle
⇒ Number of sides = = 16.36
No, we can’t have a regular polygon with each exterior angle as 22° as it is not a divisor of 360.
(b) Interior angle = 22°
Exterior angle = 180° – 22°= 158°
No, we can’t have a regular polygon with each exterior angle as 158° as it is not a divisor of 360.
6.
(a) What is the minimum interior angle possible for a regular polygon? Why?
(b) What is the maximum exterior angle possible for a regular polygon?
Solution –
(a) An equilateral triangle is the regular polygon (with 3 sides) having the least possible minimum interior angle because a regular polygon can be constructed with minimum 3 sides.
Since the sum of interior angles of a triangle = 180°
Each interior angle = 180/3 = 60°
(b) An equilateral triangle is the regular polygon (with 3 sides) having the maximum exterior angle because the regular polygon with the least number of sides has the maximum exterior angle possible. Maximum exterior possible = 180 – 60° = 120°
