Difference between revisions of "2023 AMC 10B Problems/Problem 7"
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== Solution 1== | == Solution 1== | ||
− | First, let's call the center of both squares <math>I</math>. Then, <math>\angle{AIE} = 20</math>, and since <math>\overline{EI} = \overline{AI}</math>, <math>\angle{AEI} = \angle{EAI} = 80</math>. Then, we know that <math>AI</math> bisects angle <math>\angle{DAB}</math>, so <math>\angle{BAI} = \angle{DAI} = 45</math>. Subtracting <math>45</math> from <math>80</math>, we get <math>\boxed{35 \text{B}}</math> | + | First, let's call the center of both squares <math>I</math>. Then, <math>\angle{AIE} = 20</math>, and since <math>\overline{EI} = \overline{AI}</math>, <math>\angle{AEI} = \angle{EAI} = 80</math>. Then, we know that <math>AI</math> bisects angle <math>\angle{DAB}</math>, so <math>\angle{BAI} = \angle{DAI} = 45</math>. Subtracting <math>45</math> from <math>80</math>, we get <math>\boxed{35 \text{(B)}}</math> |
Revision as of 16:32, 15 November 2023
Sqrt is rotated
clockwise about its center to obtain square
, as shown below(Please help me add diagram and then remove this). 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