2023 AMC 10B Problems/Problem 7
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 , .
~hpotter2021