(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) Consider a regular polygon having the least number of sides (i.e., an equilateral triangle)

We know that the sum of all the angles of a triangle = 180°

x + x + x = 180°

3x = 180°

x = 180° / 3

x = 60°

Thus, the minimum interior angle possible for a regular polygon = 60°

(b) We know that the exterior angle and an interior angle will always form a linear pair. Thus, the exterior angle will be maximum when the interior angle is minimum.

Consider the interior angle to be 60° since an equilateral triangle is a regular polygon having maximum exterior angle because it consists of the least number of sides

Exterior angle = 180° - 60°

= 120°

Therefore, the maximum exterior angle possible for a regular polygon is 120°.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

(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?

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.2 Question 6

Summary:

(a) The minimum interior angle possible for a regular polygon is 60°. (b) The maximum exterior angle possible for a regular polygon is 120°. 

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