Problem: In the figure AB=AC, angle BAD=30∘, and AE=AD. Then x equals:
Answer Choices:
A. 721​∘
B. 10∘
C. 1221​∘
D. 15∘
E. 20∘
Solution:
Let ∠DAE=a. Then ∠BCA=21​(180−30−a)=75−(a/2) and ∠DEA=21​(180−a)=90−(a/2)=∠ADE.
a+∠ADE+x+∠BCA=180;∴x=15 (degrees).
