Question

Square $ABCD$ is rotated $20^\circ$ clockwise about its center to obtain square $EFGH,$ as shown below. What is the degree measure of $\angle EAB?$

$24^\circ$

$35^\circ$

$30^\circ$

$32^\circ$

$20^\circ$

Answer: B

Concepts:angle chasing isosceles triangle transformation

Difficulty rating: 1310

Small Hint:

Let $O$ be the center; then $OA = OE$ and $\angle AOE = 20^\circ$

Big Hint:

Triangle $OAE$ is isosceles, and the diagonal $AO$ makes a $45^\circ$ angle with $AB$

Solution:

Let $O$ be the shared center. The rotation carries $A$ to $E,$ so $OA = OE$ and $\angle AOE = 20^\circ.$ That makes triangle $OAE$ isosceles, with base angles $\angle OAE = \frac{180^\circ - 20^\circ}{2} = 80^\circ.$ The diagonal $AC$ splits the right angle at $A,$ so $\angle OAB = 45^\circ.$ Subtracting, $\angle EAB = 80^\circ - 45^\circ = 35^\circ.$ Thus, B is the correct answer.

2023 AMC 10B Problem 7

Answer: B

Difficulty rating: 1310

Small Hint:

Big Hint:

Solution:

Problem 7 in Other Years