Problem:
In △ABC,D is a point on side AC such that BD=DC and ∠BCD measures 70∘. What is the degree measure of ∠ADB?
Answer Choices:
A. 100
B. 120
C. 135
D. 140
E. 150
Solution:
Triangle BCD is isosceles, so ∠BCD=∠CBD=70∘ and ∠BDC=180∘−2⋅70∘=40∘. Hence ∠ADB=180∘−40∘=140∘.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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