NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2.

• Understanding Quadrilaterals Class 8 Ex 3.1
• Understanding Quadrilaterals Class 8 Ex 3.3
• Understanding Quadrilaterals Class 8 Ex 3.4

Board	CBSE
Textbook	NCERT
Class	Class 8
Subject	Maths
Chapter	Chapter 3
Chapter Name	Understanding Quadrilaterals
Exercise	Ex 3.2
Number of Questions Solved	6
Category	NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

Question 1.
Find x in the following figures.

Solution.
We know that the sum of the exterior angles formed by producing the sides of a convex polygon in the same order is equal to 360°. Therefore,
(a) x + 125° + 125° = 360°
⇒ x + 250° = 360°
⇒ x = 360° – 250° = 110°
(b) x + 90° +60° + 90° + 70° = 360°
⇒  x + 310° = 360°
⇒  x = 360° – 310° = 50°

Question 2.
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Solution.
(i) Each exterior angle of a regular polygon of 9 sides

(ii) Each exterior angle of a regular polygon of 15 sides

Question 3.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution.
Since the number of sides of a regular polygon

Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution.
Let there be n sides of the polygon. Then, its each interior angle

Thus, there are 24 sides of the polygon.

Question 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) Since the number of sides of a regular polygon

= ,
Which is not a whole number.
A regular polygon with measure of each exterior angle as 22° is not possible.

(b) If interior angle = 22°, then its exterior angle = 180° – 22° = 158°.
But 158 does not divide 360 exactly.
Hence, the polygon is not possible.

Question 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) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle = 60°.
(b) Since the minimum interior angle of a regular polygon is equal to 60°, therefore, the maximum exterior angle possible for a regular polygon = 180° – 60° – 120°.

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