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2003 AIME I Problems/Problem 10: Difference between revisions

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== Problem ==
== Problem ==
Triangle <math> ABC </math> is isosceles with <math> AC = BC </math> and <math> \angle ACB = 106^\circ. </math> Point <math> M </math> is in the interior of the triangle so that <math> \angle MAC = 7^\circ </math> and <math> \angle MCA = 23^\circ. </math> Find the number of degrees in <math> \angle CMB. </math>
[[Triangle]] <math> ABC </math> is [[isosceles triangle | isosceles]] with <math> AC = BC </math> and <math> \angle ACB = 106^\circ. </math> Point <math> M </math> is in the interior of the triangle so that <math> \angle MAC = 7^\circ </math> and <math> \angle MCA = 23^\circ. </math> Find the number of degrees in <math> \angle CMB. </math>


== Solution ==
== Solution ==
 
{{solution}}
== See also ==
== See also ==
* [[2003 AIME I Problems/Problem 9 | Previous problem]]
* [[2003 AIME I Problems/Problem 11 | Next problem]]
* [[2003 AIME I Problems]]
* [[2003 AIME I Problems]]

Revision as of 15:01, 13 October 2006

Problem

Triangle $ABC$ is isosceles with $AC = BC$ and $\angle ACB = 106^\circ.$ Point $M$ is in the interior of the triangle so that $\angle MAC = 7^\circ$ and $\angle MCA = 23^\circ.$ Find the number of degrees in $\angle CMB.$

Solution

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See also