Analyzing One-Variable Relationships in Context

It's given that the sum of all interior angles in a pentagon is $540^{\circ }.$ Therefore, we can write an equation that adds all of the angles together and that is equal to $540^{\circ }.$ Note that the right angle measures $90^{\circ }.$ $$\begin{array}{c}2b+(b+20^{\circ })+(2b-20^{\circ })+b+90^{\circ }=540^{\circ }\end{array}$$ Solving this equation for $b$ will give us the measure of the unknown angle. Now, we can determine the measures of the other angles.

Given Angle	$b=75^{\circ }$	Calculate
$2b$	$2\cdot 75^{\circ }$	$150^{\circ }$
$b+20^{\circ }$	$75^{\circ }+20^{\circ }$	$95^{\circ }$
$2b-20^{\circ }$	$2\cdot 75^{\circ }-20^{\circ }$	$130^{\circ }$

Therefore, the angles in the pentagon are $75^{\circ },$ $90^{\circ },$ $95^{\circ },$ $130^{\circ },$ and $150^{\circ }.$