2007 AMC 10B Problems/Problem 4: Difference between revisions
No edit summary |
|||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
==Problem | ==Problem == | ||
The point <math>O</math> is the center of the circle circumscribed about <math>\triangle ABC,</math> with <math>\angle BOC=120^\circ</math> and <math>\angle AOB=140^\circ,</math> as shown. What is the degree measure of <math>\angle ABC?</math> | The point <math>O</math> is the center of the circle circumscribed about <math>\triangle ABC,</math> with <math>\angle BOC=120^\circ</math> and <math>\angle AOB=140^\circ,</math> as shown. What is the degree measure of <math>\angle ABC?</math> | ||
| Line 16: | Line 16: | ||
Therefore, the measure of <math>\text{arc}AC</math> is also <math>100^\circ.</math> Since the measure of an [[inscribed angle]] is equal to half the measure of the arc it intercepts, <math>\angle ABC = \boxed{\textbf{(D)} 50}</math> | Therefore, the measure of <math>\text{arc}AC</math> is also <math>100^\circ.</math> Since the measure of an [[inscribed angle]] is equal to half the measure of the arc it intercepts, <math>\angle ABC = \boxed{\textbf{(D)} 50}</math> | ||
== See Also == | |||
{{AMC10 box|year=2007|ab=B|num-b=3|num-a=5}} | |||
{{MAA Notice}} | |||
Latest revision as of 11:19, 4 July 2013
Problem
The point 
is the center of the circle circumscribed about 
with 
and 
as shown. What is the degree measure of 
Solution
Because all the central angles of a circle add up to 
Therefore, the measure of 
is also 
Since the measure of an inscribed angle is equal to half the measure of the arc it intercepts, 
See Also
| 2007 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 10 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America. 
