If the ratio of the exterior angle and interior angle of a regular polygon is 2: 3, the the polygon has ____ sides.

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Solution

The correct option is C
10

It is given that the polygon is regular.

Let exterior angle = 2x° and Interior angle = 3x°

In a regular polygon,

interior angle + exterior angle = 180°

3x + 2x = 180°

5x = 180°

x = 36°

Number of sides (n) = $\frac{360 °}{e x t e r i o r a n g l e}$

= $\frac{360 °}{36 °}$

= 10

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