2007 AMC 12B Problems/Problem 3

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 $\angle ABC$ ?

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

Solution

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

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

2007 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2007 AMC 12B Problems/Problem 3

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