Question

The measure of each interior angle of a regular polygon is 150 find the number of sides

Answer 1

The interior angle of the regular polygon =

$150^{\circ}$

Therefore, the exterior angle has measure

$180^{\circ}-150^{\circ}=30^{\circ}$

Regular polygons have the property that the sum of all its exterior angles is,

$360^{\circ}^{}^{}$

we have the formula that,

$\text{number of sides = }\frac{\sum ^{}_{}\text{ of the exterior angle}}{\text{measure of one exterior angle}}$

Thus,

$\begin{gathered} \text{number of sides = }\frac{360}{30} \\ =12 \end{gathered}$

Hence, the number of sides in the regular polygon is 12.