Question

If each interior angle of a regular polygon is 10 times its exterior angle, the number of sides of the polygon is

Answer 1

the exterior angle of the regular polygon is equal to 360 / number of sides. solve for number of sides to get number of sides = 360 / exterior angle = 360 / 36 =10. this formula becomes 144 = (180 * (n-2)) / n.

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Answer 2

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Solution:-

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interior angle + exterior angle = 180°

Exterior angle = 360°

=> Number of sides n = 360° / exterior angle

let x be the exterior angle

=> interior angle = 10x

=> 11x = 180 => x = 180 / 11

=> n = 360 / 180 / 11 = 360 × 11 / 180

=> n = 22

=> The polygon has 22 sides.

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