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 ~Aops-g5-gethsemanea2
Solution 2
Note that , meaning that the reflex of
, so
. It is given that
has two sides of equal length, so it is isosceles, thus having two congruent angles.
The sum of these two angles is , so the measure of both
and angle
is
. Since
is the supplement to
, and
,
degrees.
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.