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

#1**+1 **

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°

CPhill Jun 27, 2018