2023 AMC 10B Problem 7

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

Let

O

be the center; then

OA = OE

and

\angle AOE = 20^\circ

Triangle

OAE

is isosceles, and the diagonal

AO

makes a

45^\circ

angle with

AB

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.

Problem 7 in other years