The NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals contains solutions for all exercise questions. The subject experts at BYJU’S have solved each question of NCERT exercises meticulously to help the students in solving any question from the NCERT textbook. NCERT Class 8 Exercise 3.2 is based on the measurement of the exterior angle of a polygon. Students can download the NCERT Solutions of Class 8 Mathematics to enhance their problem-solving skills.
NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals Exercise 3.2
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Access other exercise solutions of Class 8 Maths Chapter 3 – Understanding Quadrilaterals
Exercise 3.1 Solutions 7 Questions (1 Long Answer Question, 6 Short Answer Questions)
Exercise 3.3 Solutions 12 Questions (6 Long Answer Questions, 6 Short Answer Questions)
Exercise 3.4 Solutions 6 Questions (1 Long Answer Question, 5 Short Answer Questions)
Access answers of Maths NCERT Class 8 Chapter 3 – Understanding Quadrilaterals Exercise 3.2 Page Number 44
1. Find x in the following figures.
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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 2 opposite interior 2 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 has five sides and is a pentagon.
Thus, sum of the angles of 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:
Sum of angles a regular polygon having side n = (n-2)×180°
(i) Sum of angles a regular polygon having side 9 = (9-2)×180°= 7×180° = 1260°
Each interior angle=1260/9 = 140°
Each exterior angle = 180° – 140° = 40°
Or,
Each exterior angle = sum of exterior angles/Number of angles = 360/9 = 40°
(ii) Sum of angles a regular polygon having side 15 = (15-2)×180°
= 13×180° = 2340°
Each interior angle = 2340/15 = 156°
Each exterior angle = 180° – 156° = 24°
Or,
Each exterior angle = sum of exterior angles/Number of angles = 360/15 = 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 = 360/24 = 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 = 360/15 = 24
Thus, the regular polygon has 24 sides.
5.
a) Is it possible to have a regular polygon with the 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 = 360/22 = 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) Equilateral triangle is a regular polygon with 3 sides. It has the least possible minimum interior angle because a regular polygon with minimum sides can be constructed with 3 sides at least. The sum of interior angles of a triangle = 180°
Each interior angle = 180/3 = 60°
b) Equilateral triangle is a regular polygon with 3 sides that has 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°
Exercise 3.2 of NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals is based on the sum of the measures of the exterior angles of a polygon. By practising these questions regularly, students will improve their time management skills and also increase their confidence.
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