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The interior angle of a regular polygon is 6 times its exter...

The interior angle of a regular polygon is 6 times its exterior angle find the number of sides of the polygon.

A.

12

B.

15

C.

10

D.

14

View answer & explanation

Correct answer is D

each interior angle of a polygon = $\frac{(n - 2)\times 180}{n}$ where n = no of side of a polygon

each exterior angle of a polygon = $\frac{360}{n}$

then $\frac{(n - 2)\times 180}{n}$ = 6 $\times$ $\frac{360}{n}$

= (n - 2) 180 = 2160

= 180n - 360 = 2160

= 180n = 2160 + 360

= 180n = 2520

therefore, n = $\frac{2520}{180}$ = 14.

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