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Question

The ratio between the interior angle and the exterior angle of a regular polygon is $$2:1$$. Find:
number of sides in the polygon.

Solution
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Interior angle : exterior angle = 2 : 1
Let interior angle = 2x° & exterior angle = x°

∴ 2x° + x° = 180°

3x = 180°

(i) x = 60°

∴ Each exterior angle = 60°

Let no. of sides = n

∴ 360° /n = 60°

n = 360° /60°

n = 6

(ii)

∴ (i) 60° (ii) 6


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