Difference between revisions of "2023 AMC 10B Problems/Problem 7"
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Call the center of both squares point <math>O</math>, and draw circle <math>O</math> such that it circumscribes the squares. <math>\angle{EOF} = 90</math> and <math>\angle{BOF} = 20</math>, so <math>\angle{EOB} = 70</math>. Since <math>\angle{EAB}</math> is inscribed in arc EB, <math>\angle{EAB} = 70/2 = \boxed{\text{(B)} 35}</math>. | Call the center of both squares point <math>O</math>, and draw circle <math>O</math> such that it circumscribes the squares. <math>\angle{EOF} = 90</math> and <math>\angle{BOF} = 20</math>, so <math>\angle{EOB} = 70</math>. Since <math>\angle{EAB}</math> is inscribed in arc EB, <math>\angle{EAB} = 70/2 = \boxed{\text{(B)} 35}</math>. | ||
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~hpotter2021 | ~hpotter2021 |
Revision as of 20:27, 15 November 2023
Square is rotated
clockwise about its center to obtain square
, as shown below.
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)
Solution 3
Call the center of both squares point , and draw circle
such that it circumscribes the squares.
and
, so
. Since
is inscribed in arc EB,
.
~hpotter2021