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2007 AMC 12B Problems/Problem 3

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Problem

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?

Image:2007_12B_AMC-3.png

\mathrm {(A)} 35 \qquad \mathrm {(B)} 40 \qquad \mathrm {(C)} 45 \qquad \mathrm {(D)} 50 \qquad  \mathrm {(E)} 60

Solution

\angle AOC=360-140-120=100=2\angle ABC

\angle ABC=50 \Rightarrow \mathrm {D}

See Also

2007 AMC 12B (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
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Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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