Question

8. The measure of an intererangle of a regular polygon is135°. Find the number of sides.

Answer 1

The sum of the interior angles of a polygon is given by:

`\text{Sum}=(n-2)*180`

Where n is the number of sides.

When we divide the sum by the number of sides we obtain the measure of each interior angle, then:

`(Sum)/(n)=135`

By replacing the sum by the formula we can solve for n:

`\begin{gathered} ((n-2)*180)/(n)=135 \\ (n-2)*180=135n \\ \text{Apply the distributive property} \\ 180n-360=135n \\ 180n-135n=360 \\ 45n=360 \\ n=(360)/(45) \\ n=8 \end{gathered}`

Thus, the number of sides of the regular polygon is 8.