Difference between revisions of "2021 Fall AMC 12A Problems/Problem 6"
MRENTHUSIASM (talk | contribs) (Sorry to undo the progress. In the new Solution 2, the point G is defined, but not used in the solution, so I think there's no need to make things more complicated.) |
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~Charles3829 | ~Charles3829 | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/T4NhPER6SrM | ||
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+ | ~Lucas | ||
==See Also== | ==See Also== |
Revision as of 02:27, 17 August 2022
- The following problem is from both the 2021 Fall AMC 10A #7 and 2021 Fall AMC 12A #6, so both problems redirect to this page.
Contents
[hide]Problem
As shown in the figure below, point lies on the opposite half-plane determined by line from point so that . Point lies on so that , and is a square. What is the degree measure of ?
Solution
By angle subtraction, we have Note that is isosceles, so Finally, we get degrees.
~MRENTHUSIASM ~Aops-g5-gethsemanea2
Video Solution by TheBeautyofMath
for AMC 10: https://youtu.be/ycRZHCOKTVk?t=232
for AMC 12: https://youtu.be/wlDlByKI7A8
~IceMatrix
Video Solution by WhyMath
~savannahsolver
Video Solution by HS Competition Academy
~Charles3829
Video Solution
~Lucas
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
2021 Fall AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.