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The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find the number of sides in the polygon.
1. 6
2. 7
3. 5
4. 8

1 Answer

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Correct Answer - Option 1 : 6

Given

The ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1

Concept

Exterior angle + interior angle = 180° 

Side of polygon = (360°/Exterior angle)

Calculation

Let ratio of angles in x 

⇒ The ratio between the interior angle and the exterior angle of a regular polygon is = 2x : x

⇒ 2x + x = 180°

⇒ 3x = 180°

⇒ x = (180°/3)

⇒ x = 60°

⇒ Interior angle = 120°

⇒ Exterior angle = 60°

⇒ Side of polygon = (360°/60°)

⇒ Side of polygon = 6

∴ Side of polygon = 6

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