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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$?

Guest Jun 27, 2018
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The interior angles of a pentagon will sum to 540°

 

So  we have that

 

A  = D - 40  

B  = D - 40

C  = D - 40

E  = D

 

So we have that

 

A + B + C + D + E  = 540      and substituting, we have

 

D - 40  + D - 40  + D - 40 + D  + D  = 540    simplify

 

5D - 120  = 540     add 120 to both sides

 

5D  =  660     divide both sides by 5

 

D  =  132°

 

 

cool cool cool

CPhill  Jun 27, 2018

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