2020 AIME I Problems/Problem 1
Contents
[hide]Problem
In with point lies strictly between and on side and point lies strictly between and on side such that The degree measure of is where and are relatively prime positive integers. Find
Solution 1
If we set to , we can find all other angles through these two properties: 1. Angles in a triangle sum to . 2. The base angles of an isoceles triangle are congruent.
Now we angle chase. , , , , , . Since as given by the problem, , so . Therefore, , and our desired angle is for an answer of .
-molocyxu
Solution 2
Let be . . By Exterior Angle Theorem on triangle , . By Exterior Angle Theorem on triangle , . This tells us Thus and we want to get an answer of .
See Also
2020 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 2 | |
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