AMC 8 2014 Problem 9

AMC8 2014 年第 9 题

三角形★★☆☆☆
In △ABC\bigtriangleup ABC, D is a point on side AC‾\overline{AC} such that BD=DC and ∠BCD\angle BCD measures 70∘70^\circ. What is the degree measure of ∠ADB\angle ADB?
在 △ABC\triangle ABC 中，DD 是边 AC‾\overline{AC} 上一点，使得 BD=DC，且 ∠BCD=70∘\angle BCD = 70^\circ。那么 ∠ADB\angle ADB 的度数是多少？
AMC 8 2014 Problem 9 figure
  1. A.100
  2. B.120
  3. C.135
  4. D.140
  5. E.150

正确答案 · Correct Answer

D

解析 · Solution

Solution 1

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

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