2021 Fall AMC 10A Problems/Problem 7
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
Solution 2 (same as Solution 1 but by another user)
Since and
we know that
From the given,
so that means
is isosceles. So,
Hence,
since it is supplementary to
This gives us answer choice
Aops-g5-gethsemanea2 (talk) 18:56, 22 November 2021 (EST) This solution conflicted with the above solution due to two people editing at the same time.
See Also
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 |
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