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 = }(360)/(30) \\ =12 \end{gathered}`

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