Question

find the number of sides of a regular polygon if each interior angle is 165 also find the number of diagonals and each exterior angle

Answer 1

(I) No. of sides

165 = 180(n-2)/n
after solving this equation
n=24

(ii) Each ext. angle = 360/n= 360/24 = 15

(iii) no. of diagonal = n(n-3)/2 = 24*21/2 = 252