Difference between revisions of "2020 AIME I Problems/Problem 1"
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If we set <math>\angle{BAC}</math> to <math>x</math>, we can find all other angles through these two properties: | If we set <math>\angle{BAC}</math> to <math>x</math>, we can find all other angles through these two properties: | ||
1. Angles in a triangle sum to <math>180^{\circ}</math>. | 1. Angles in a triangle sum to <math>180^{\circ}</math>. |
Revision as of 17:09, 12 March 2020
Note: Please do not post problems here until after the AIME.
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
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
.
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.