Question

1. What is the minimum interior angle possible for a regular polygon? Why? 
2. What is the maximum exterior angle possible for a regular polygon?

Answer 1

(a) Consider a regular polygon having the lowest possible number of sides (i.e., an equilateral triangle). 
The exterior angle of this triangle will be the maximum exterior angle possible for any regular polygon.
Exterior angle of an equilateral triangle 
= \(\frac{360°}{3}\) 
= \(120°\)

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(b)Hence, maximum possible measure of exterior angle for any polygon is \(120\degree\). 
Also, we know that an exterior angle and an interior angle are always in a linear pair.
Hence, minimum interior angle 
= \(180 º - 120°\) 
= \(60\degree\)