AMC12 2007 A

AMC12 2007 A · Q6

AMC12 2007 A · Q6. It mainly tests Angle chasing, Triangles (properties).

Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$. Point $D$ is inside triangle $ABC$, angle $ABC$ measures $40$ degrees, and angle $ADC$ measures $140$ degrees. What is the degree measure of angle $BAD$?

等腰三角形 $ABC$ 和 $ADC$ 满足 $AB=BC$ 且 $AD=DC$。点 $D$ 在三角形 $ABC$ 内部，$\angle ABC$ 的度数为 $40$，且 $\angle ADC$ 的度数为 $140$。$\angle BAD$ 的度数是多少？

(A) 20 20

(B) 30 30

(D) 50 50

(E) 60 60

Answer

Correct choice: (D)

正确答案：（D）

Solution

Error creating thumbnail: Unable to save thumbnail to destination We angle chase and find out that: - $\angle DAC=\frac{180-140}{2} = 20$ - $\angle BAC=\frac{180-40}{2} = 70$ - $\angle BAD=\angle BAC- \angle DAC=50\ \mathrm{(D)}$

通过追角可得： - $\angle DAC=\frac{180-140}{2} = 20$ - $\angle BAC=\frac{180-40}{2} = 70$ - $\angle BAD=\angle BAC- \angle DAC=50\ \mathrm{(D)}$

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