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The interior angle of a regular polygon is five times the...

The interior angle of a regular polygon is five times the size of its exterior angle. Identify the polygon.

A.

dodecagon

B.

enneadecagon

C.

icosagon

D.

hendecagon

Correct answer is A

An interior angle of a regular polygon = (2n4)×90n

An exterior angle of a regular polygon = 360n

(2n4)×90n =5 ×  360n (Given)
= (2n-4) x 90 = 5 x 360
= 180n - 360 = 1800
= 180n = 1800 + 360
= 180n = 2160
= n = 2160180 = 12
The polygon has 12 sides which is dodecagon