AMC12 2007 B

AMC12 2007 B · Q7

AMC12 2007 B · Q7. It mainly tests Triangles (properties), Circle theorems.

All sides of the convex pentagon $ABCDE$ are of equal length, and $\angle A = \angle B = 90^{\circ}$. What is the degree measure of $\angle E$?

凸五边形 $ABCDE$ 的所有边长相等，且 $\angle A = \angle B = 90^{\circ}$。$\angle E$ 的度数是多少？

(A) 90 90

(B) 108 108

(D) 144 144

(E) 150 150

Answer

Correct choice: (E)

正确答案：（E）

Solution

Error creating thumbnail: Unable to save thumbnail to destination Since $A$ and $B$ are right angles, and $AE$ equals $BC$, and $AECB$ is a square. Since the length of $ED$ and $CD$ are also 5, triangle $CDE$ is equilateral. Angle $E$ is therefore $90+60=150 \Rightarrow \mathrm {(E)}$

由于 $A$ 和 $B$ 是直角，且 $AE$ 等于 $BC$，所以 $AECB$ 是一个正方形。又因为 $ED$ 和 $CD$ 的长度也都是 5，所以三角形 $CDE$ 是等边三角形。因此 $\angle E$ 为 $90+60=150 \Rightarrow \mathrm {(E)}$

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