Question

An exterior angle and an interior angle of a regular polygon are in the ratio 2 : 7. The number of sides in the polygon is ______.

Options

• 12

• 6

• 4

• 9

Answer 1

An exterior angle and an interior angle of a regular polygon are in the ratio 2 : 7. The number of sides in the polygon is 9.

Explanation:

Since an exterior angle and its corresponding interior angle are supplementary, let them be 2x and 7x such that 2x + 7x = 180°, giving x = 20°. The exterior angle is 2(20°) = 40°, and the number of sides in the regular polygon is calculated as `\frac{360^\circ}{40^\circ} = 9`.