standard_description: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
problem_activity: Task
In triangle $\Delta ABC$, point $M$ is the point of intersection of the bisectors of angles $\angle BAC$, $\angle ABC$, and $\angle ACB$.  The measure of $\angle ABC$ is $42^\circ$, and the measure of $\angle BAC$ is $64^\circ$.  What is the measure of $\angle BMC$?
[IMG]
This task adapted from a problem published by the Russian Ministry of Education.


aligns: yes