AMC10 2023 B

AMC10 2023 B · Q7

AMC10 2023 B · Q7. It mainly tests Angle chasing, Transformations.

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

正方形 $ABCD$ 围绕其中心顺时针旋转 $20^{\circ}$ 得到正方形 $EFGH$，如下图所示。$\angle EAB$ 的度数是多少？ $\text{

(A) \ 24^{\circ} \ 24^{\circ}

(B) \ 35^{\circ} \ 35^{\circ}

(D) \ 32^{\circ} \ 32^{\circ}

(E) \ 20^{\circ} \ 20^{\circ}

Answer

Correct choice: (B)

正确答案：（B）

Solution

First, let's call the center of both squares $I$. Then, $\angle{AIE} = 20$, and since $\overline{EI} = \overline{AI}$, $\angle{AEI} = \angle{EAI} = 80$. Then, we know that $AI$ bisects angle $\angle{DAB}$, so $\angle{BAI} = \angle{DAI} = 45$. Subtracting $45$ from $80$, we get $\boxed{\text{(B)} 35}$

首先，将两个正方形的中心称为 $I$。则 $\angle{AIE} = 20$，并且由于 $\overline{EI} = \overline{AI}$，$\\angle{AEI} = \\angle{EAI} = 80$。然后，我们知道 $AI$ 平分角 $\angle{DAB}$，所以 $\angle{BAI} = \angle{DAI} = 45$。80 减去 45，得 $\boxed{\text{(B)} 35}$

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