Grades 11-12 Video Solutions 2010-11&12 Video Solutions 2010 problem6

Video Transcription

Question number six. Triangle ABC is a right triangle. Point M is the midpoint of its hypotenuse and the measure of angle BAC is 60 degrees. What is the  measure of angle BMC? In our diagram here we can label that information. You can read the problem again. ABC is a right triangle so at point C here we have a 90  degree angle. Point M is the midpoint of the hypotenuse so the segments AM and BM are equal in length and the measure of angle BAC is 60 degrees which is labeled  here already. Now what we can do is we can easily figure out the measure of angle here at vertex B that has to be 30 degrees and then we can bisect the  segment BC with the following line here that I drew in blue. Let me call the point of intersection here N. We have a 90 degree angle over here that is a  bisector of the segment BC so let me label that here in blue. These segments BN and CN are equal in length and so what we have now are triangles BMN and  the second triangle below CMN are in fact congruent and this is by the side  angle side congruency which should be apparent here from the picture side CN BN the 90 degree angle and the side NM in common and with that we can compute  the measure of the angle here measure of the angle BMN here is equal to 60 degrees and so likewise the measure of the angle CMN is 60 degrees so we can  then say that the measure of the angle BMC is equal to the measure of the angle BMN plus the measure of the angle CMN both of them are equal to 60  degrees and so we have our answer 120 degrees is the measure of the angle BMC and that is answer D.

Video Summary

Summary Not Available