Answer:
Angle BCA is 74 degrees, angle MBC is 21, angle MCB is 37, and BMC is 122
Step-by-step explanation:
First off, MBC was an angle that was bisected by point M, meaning that if you took half of angle ABC, you would get your answer.
(0.5)(42)=21
Since you already have two angle measures, being ABC and BAC, you can find angle BCA by adding the two angle measures up, then subtracting by 180 to get your answer:
180=64+42+BCA, which your answer will be 74 degrees.
Now that you have found angle BCA, you take half of that angle measure to then find angle MCB, because point M bisected angles ABC, BAC, and BCA.
(0.5)(74)=37
Finally, since you have found the angles MBC and MCB, in order to find angle BMC you will have to do the same application for BCA:
180=21+37+BMC, which your answer will be 122 degrees.
Hope this helps!
