Question

If the measure of each interior angle of a regular polygon is 150 then its number of diagonals willbe

Answer 1

look let the no. of sides be n then
(2n-4)90=150n
n will be 12
now diagonals is given by
$\frac{n(n - 3)}{2}$
put n 12 and your answer is 54

Answer 2

Answer

A = 180(n-2)/n

150 = 180(n-2)/n

150n = 180n - 360

360 = 30n

n = 12