AMC12 2007 B
AMC12 2007 B · Q3
AMC12 2007 B · Q3. It mainly tests Angle chasing, Circle theorems.
The point $O$ is the center of the circle circumscribed about triangle $ABC$, with $\angle BOC = 120^{\circ}$ and $\angle AOB = 140^{\circ}$, as shown. What is the degree measure of $\angle ABC$?
点 $O$ 是三角形 $ABC$ 的外接圆圆心，且 $\angle BOC = 120^{\circ}$、$\angle AOB = 140^{\circ}$，如图所示。$\angle ABC$ 的度数是多少？
(A)
35
35
(B)
40
40
(C)
45
45
(D)
50
50
(E)
60
60
Answer
Correct choice: (D)
正确答案：（D）
Solution
Since triangles $ABO$ and $BOC$ are isosceles, $\angle ABO=20^o$ and $\angle OBC=30^o$. Therefore, $\angle ABC=50^o$, or $\mathrm{(D)}$.
由于三角形 $ABO$ 和 $BOC$ 是等腰三角形，$\angle ABO=20^o$ 且 $\angle OBC=30^o$。因此 $\angle ABC=50^o$，即 $\mathrm{(D)}$。
Topics
Related Questions
Practice full AMC exams on amcdrill.
Try full-length practice and diagnostics at www.amcdrill.com.