Difference between revisions of "2007 AMC 12B Problems/Problem 3"

m (Solution: making answer more obvious)
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<math>\angle AOC=360-140-120=100=2\angle ABC</math>
 
<math>\angle AOC=360-140-120=100=2\angle ABC</math>
  
<math>\angle ABC=50 \Rightarrow \mathrm {D}</math>
+
<math>\angle ABC=50 \Rightarrow \boxed{\mathrm {D}}</math>
  
 
==See Also==
 
==See Also==

Revision as of 12:44, 21 January 2015

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 $\angle ABC$?

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

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

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

See Also

2007 AMC 12B (ProblemsAnswer KeyResources)
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
All AMC 12 Problems and Solutions

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