Q. The interior angles of a regular polygon measure 160${^\circ}$ each. The number of diagonals of the polygon are
A) 97
B) 105
C) 135
D) 146
Explanation
(c)
Let $n$ be the number of sides of the polygon
$n.160{^\circ} = (n - 2).180{^\circ}$
$\Rightarrow 20{^\circ}.n = 360{^\circ}$
$\therefore\ n = 18$
Then number of diagonals $= \ ^{18}C_{2} - 18 = 153 - 18 = 135$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.