Question

The interior angles of a regular polygon are each 150° .Calculate the no. of sides .

Answer 1

$\boxed {\text {Interior Angle = }\dfrac{(n-2) \times 180}{n} }$

Given that interior angle = 150°

$\dfrac{(n-2) \times 180}{n} = 150$

Solve n:

$(n-2) \times 180= 150n$

$180n - 360= 150n$

$180n - 150n = 360$

$30n = 360$

$n = 12$

Answer: There are 12 sides.