Problem:
If ∠A=60∘,∠E=40∘ and ∠C=30∘, then ∠BDC=
Answer Choices:
A. 40∘
B. 50∘
C. 60∘
D. 70∘
E. 80∘
Solution:
Since the sum of the angles in any triangle is 180∘,
∠ABE=180∘−(60∘+40∘)=80∘.
Since ∠ABD and ∠DBC together form a straight angle, their sum is 180∘, so ∠DBC=180∘−80∘=100∘. Thus ∠BDC=180∘−(100∘+30∘)=50∘.
Answer: B.
The problems on this page are the property of the MAA's American Mathematics Competitions
