2007 AMC 10B Problem 7

Question

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?

90

108

120

144

150

Two right angles at adjacent vertices make part of the figure a square

ABCE

is a square and

\triangle CDE

is equilateral

Because

AB=BC=EA

and

\angle A=\angle B=90^\circ,

quadrilateral

ABCE

is a square, so

\angle AEC=90^\circ.

The remaining sides satisfy

CD=DE=EC,

so

\triangle CDE

is equilateral and

\angle CED=60^\circ.

Therefore

\angle E=\angle AEC

+\angle CED=90^\circ

+60^\circ=150^\circ.

Thus, the correct answer is E.

Problem 7 in other years