Problem: In triangle ABC,AB=AC and ∠A=80∘. If points D,E and F lie on sides BC, AC and AB, respectively, and CE=CD and BF=BD, then ∠EDF equals
Answer Choices:
A. 30∘
B. 40∘
C. 50∘
D. 65∘
E. none of these
Solution:
∠B=∠C=50∘;∠CDE=∠FDB=65∘;∠EDF=180∘−2(65∘)=50∘. Note: The measure of ∠EDF is 50∘ even if ABî€ =AC :
∠EDF​=180∘−∠CDE−∠FDB=180∘−1/2(180∘−∠C)−1/2(180∘−∠B)=1/2(∠B+∠C)=1/2(180∘−∠A)=50∘.​
