It's given that the sum of all interior angles in a pentagon is
540∘. Therefore, we can write an equation that adds all of the angles together and that is equal to
540∘. Note that the measures
90∘.
2b+(b+20∘)+(2b−20∘)+b+90∘=540∘
Solving this equation for
b will give us the measure of the unknown angle.
2b+(b+20∘)+(2b−20∘)+b+90∘=540∘
2b+b+20∘+2b−20∘+b+90∘=540∘
2b+2b+b+b+90∘+20∘−20∘=540∘
6b+90∘=540∘
6b=450∘
b=75∘
Now, we can determine the measures of the other angles.
Given Angle
|
b=75∘
|
Calculate
|
2b
|
2⋅75∘
|
150∘
|
b+20∘
|
75∘+20∘
|
95∘
|
2b−20∘
|
2⋅75∘−20∘
|
130∘
|
Therefore, the angles in the pentagon are 75∘, 90∘, 95∘, 130∘, and 150∘.