2007 AMC 12B Problems/Problem 7

Problem

All sides of the convex pentagon $ABCDE$ are of equal length, and $\angle A = \angle B = 90^{\circ}$ . What is the degree measure of $\angle E$ ?

$\mathrm {(A)} 90$ $\mathrm {(B)} 108$ $\mathrm {(C)} 120$ $\mathrm {(D)} 144$ $\mathrm {(E)} 150$

Solution

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Since $A$ and $B$ are right angles, and $AE$ equals $BC$ , $AECB$ is a square, and $EC$ is 5. Since $ED$ and $CD$ are also 5, triangle $CDE$ is equilateral. Angle $E$ is therefore $90+60=150 \Rightarrow \mathrm {(E)}$

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2007 AMC 12B Problems/Problem 7

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