Question

Find out if it is possible to have a regular polygon with each interior angle equal to ${150}^0$. (Enter 1 if possible, else 0)

Answer 1

The sum of measures in a convex polygon with 'n' sides is

$S={180}^{\circ }(n-2)$

When the polygon is regular, all of its angles are equal so to find the measure of one interior angle, we divide by n:

$150=\frac{{180}^{\circ }(n-2)}{n}$

$150n=180n-{360}^{\circ }$

$30n={360}^{\circ }$

$n=12$

This is an integer, so a regular polygon with 12 sides would have interior angles measuring ${150}^{\circ }$.

Therefore correct answer is $1$.