Difference between revisions of "2020 AIME I Problems/Problem 1"
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https://artofproblemsolving.com/wiki/index.php/1961_AHSME_Problems/Problem_25 | https://artofproblemsolving.com/wiki/index.php/1961_AHSME_Problems/Problem_25 | ||
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+ | See here for a video solution: | ||
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+ | https://youtu.be/4XkA0DwuqYk | ||
==See Also== | ==See Also== |
Revision as of 18:55, 6 April 2020
Contents
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 .
Solution 2
Let be in degrees. . By Exterior Angle Theorem on triangle , . By Exterior Angle Theorem on triangle , . This tells us and . Thus and we want to get an answer of .
https://artofproblemsolving.com/wiki/index.php/1961_AHSME_Problems/Problem_25
(Almost Mirrored)
See here for a video solution:
See Also
2020 AIME I (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.