AMC8 2014

AMC8 2014 · Q9

AMC8 2014 · Q9. It mainly tests Angle chasing, Triangles (properties).

In $\bigtriangleup ABC$, $D$ is a point on side $\overline{AC}$ such that $BD=DC$ and $\angle BCD$ measures $70^\circ$. What is the degree measure of $\angle ADB$?

在$\bigtriangleup ABC$中，点$D$在边$\overline{AC}$上，使得$BD=DC$且$\angle BCD$的度数为$70^\circ$。求$\angle ADB$的度数。

(A) 100 100

(B) 120 120

(D) 140 140

(E) 150 150

Answer

Correct choice: (D)

正确答案：（D）

Solution

Using angle chasing is a good way to solve this problem. $BD = DC$, so $\angle DBC = \angle DCB = 70$, because it is an isosceles triangle. Then $\angle CDB = 180-(70+70) = 40$. Since $\angle ADB$ and $\angle BDC$ are supplementary, $\angle ADB = 180 - 40 = \boxed{\textbf{(D)}~140}$.

使用角度追踪法是解决此题的好方法。因为$BD = DC$，所以$\angle DBC = \angle DCB = 70^\circ$，因为这是一个等腰三角形。然后$\angle CDB = 180 - (70 + 70) = 40^\circ$。由于$\angle ADB$和$\angle BDC$互补，故$\angle ADB = 180 - 40 = \boxed{\textbf{(D)}~140}$。

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