Question 100

Each interior angle of a regular polygon is greater than its exterior angle by $$36^\circ$$. Find the number of sides of the polygon.

Solution

In the regular polygon, interior angle (IA) = exterior angle (EA) + 36, or

EA = IA - 36.

But IA + EA = 180, or

2 IA -36 = 180

2IA = 216,

IA = 108 deg and EA = 72 deg

Number of sides of regular polygon = 360/72 = 5.

B is correct choice.

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