Problem:
∠1+∠2=180∘.
∠3=∠4.
Find ∠4.
Answer Choices:
A. 20∘
B. 25∘
C. 30∘
D. 35∘
E. 40∘
Solution:
Since the sum of the angles of a triangle is 180∘,40∘+70∘+∠1= 180∘ and ∠1=70∘. This means that ∠2=110∘. Then 110∘+∠3+∠4=180∘, so ∠3+∠4=70∘ and ∠3=∠4=35∘.
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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