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.
dodecagon
enneadecagon
icosagon
hendecagon
Correct answer is A
An interior angle of a regular polygon = (2n−4)×90n
An exterior angle of a regular polygon = 360n
(2n−4)×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
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