Problem:
In triangle CAT, we have ∠ACT=∠ATC and ∠CAT=36∘. If TR bisects ∠ATC, then ∠CRT=
Answer Choices:
A. 16∘
B. 51∘
C. 72∘
D. 90∘
E. 108∘
Solution:
Since ∠ACT=∠ATC and ∠CAT=36∘, we have 2(∠ATC)= 180∘−36∘=144∘ and ∠ATC=∠ACT=72∘. Because TR bisects ∠ATC, ∠CTR=21​(72∘)=36∘. In triangle CRT,∠CRT=180∘−36∘−72∘=72∘.
Note that some texts use ∠ACT to define the angle and m∠ACT to indicate its measure.
Answer: C​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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