Problem:
All sides of the convex pentagon ABCDE are of equal length, and ∠A=∠B= 90∘. What is the degree measure of ∠E ?
Answer Choices:
A. 90
B. 108
C. 120
D. 144
E. 150
Solution:
Because AB=BC=EA and ∠A=∠B=90∘, quadrilateral ABCE is a square, so ∠AEC=90∘.
Also CD=DE=EC, so △CDE is equilateral and ∠CED=60∘. Therefore
∠E=∠AEC+∠CED=90∘+60∘=150∘.
The problems on this page are the property of the MAA's American Mathematics Competitions
