Question

How do I find the measure of the interior angle?

Answer 1

see the explanation

Explanation:

we know that

The sum of the interior angles in any polygon is given by the formula

`S=(n-2)180^o`

where

n is the number of sides of the polygon

step 1

Find the sum of the interior angles in the given polygon

we have

`n=5\ sides`

substitute

`S=(5-2)180^o=540^o`

step 2

Find the value of x

we know that

`-3x+125+(45-x)+(-x+90)+80=540`

solve for x

`-5x+340=540`

`-5x=200\\x=-40`

step 3

Find the measure of each interior angle

substitute the value of x

Angle A

`-3(-40)=120^o`

Angle B

`80^o`

Angle C

`-(-40)+90=130^o`

Angle D

`45-(-40)=85^o`

Angle E

`125^o`