Problem:
Segment BD and AE intersect at C, as shown, AB=BC=CD=CE, and ∠A=25∠B. What is the degree measure of ∠D?
Answer Choices:
A. 52.5
B. 55
C. 57.5
D. 60
E. 62.5
Solution:
Because △ABC is isosceles, ∠A=∠C. Because ∠A=25∠B, we have 25∠B+25∠B+∠B=180∘, so ∠B=30∘. Therefore ∠ACB=∠DCE= 75∘. Because △CDE is isosceles, 2∠D+75∘=180∘, so ∠D=(A)52.5∘.
The problems on this page are the property of the MAA's American Mathematics Competitions
