Problem:
In △ABC,∠A=55∘,∠C=75∘,D is on side AB and E is on side BC. If DB=BE, then ∠BED=
Answer Choices:
A. 50∘
B. 55∘
C. 60∘
D. 65∘
E. 70∘
Solution:
We have ∠B=180∘−(55∘+75∘)=50∘. Since △BDE is isosceles, ∠BED=2180∘−∠B​=2180∘−50∘​=65∘.
