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
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.
