Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 1.9 Junior Find the answer

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 $\angle ABC$ ?
2007 12B AMC-3.png

Pick one

Solution

Since triangles $ABO$ and $BOC$ are isosceles, $\angle ABO=20^o$ and $\angle OBC=30^o$ . Therefore, $\angle ABC=50^o$ , or $\mathrm{(D)}$ .

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