Problem: In triangle ABC,AB=AC and β A=80β. If points D,E and F lie on sides BC, AC and AB, respectively, and CE=CD and BF=BD, then β EDF equals
Answer Choices:
A. 30β
B. 40β
C. 50β
D. 65β
E. none of these
Solution:
β B=β C=50β;β CDE=β FDB=65β;β EDF=180ββ2(65β)=50β. Note: The measure of β EDF is 50β even if ABξ =AC :
β EDFβ=180βββ CDEββ FDB=180ββ1/2(180βββ C)β1/2(180βββ B)=1/2(β B+β C)=1/2(180βββ A)=50β.β
