Question

How many sides has a regular polygon if it's interior angles are:144 each, 135 each

Answer 1

The measure of each interior angle of a regular polygon is
`(180(n-2))/(n)` degrees, where n is the number of sides.

Question 1

`144=(180(n-2))/(n)\\\\144n=180(n-2)\\\\144n=180n-360\\\\-36n=-360\\\\n=10 \text{ sides}`

Question 2

`(180(n-2))/(n)=135\\\\180(n-2)=135n\\\\180n-360=135n\\\\-360=-45n\\\\n=8 \text{ sides}`