Difference between revisions of "2023 AMC 10B Problems/Problem 7"
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Square <math>ABCD</math> is rotated <math>20^{\circ}</math> clockwise about its center to obtain square <math>EFGH</math>, as shown below(Please help me add diagram and then remove this). | Square <math>ABCD</math> is rotated <math>20^{\circ}</math> clockwise about its center to obtain square <math>EFGH</math>, as shown below(Please help me add diagram and then remove this). | ||
− | [[ | + | [[Image:202310bQ17.jpeg]] |
What is the degree measure of <math>\angle EAB</math>? | What is the degree measure of <math>\angle EAB</math>? | ||
Revision as of 20:16, 15 November 2023
Square is rotated
clockwise about its center to obtain square
, as shown below(Please help me add diagram and then remove this).
File:202310bQ17.jpeg
What is the degree measure of
?
Solution 1
First, let's call the center of both squares . Then,
, and since
,
. Then, we know that
bisects angle
, so
. Subtracting
from
, we get
~jonathanzhou18
Solution 2
First, label the point between and
point
and the point between
and
point
. We know that
and that
. Subtracting
and
from
, we get that
is
. Subtracting
from
, we get that
. From this, we derive that
. Since triangle
is an isosceles triangle, we get that
. Therefore,
. The answer is
.
~yourmomisalosinggame (a.k.a. Aaron)