Question

Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M. Find m∠AMB, if m∠A = 58°, m∠B = 96°.

Answer 1

103 degrees

Explanation:

Bisectors means you make a line in the middle splitting the angle in half. So you divide A by 2 to get 29 and B to get 48. Then you add them to get 77. And now you only need point m's angle. 180-77 is 103 so the answer they are looking for is 103.

Answer 2

measure angle A is 58 degrees, this means that, the angle bisector divides the angle into two equal angles each of measure 58/2 = 29 degrees

measure angle B is 96 degrees, this means that the angle bisector divides the angle into two equal angles each of measure 96/2 = 48 degrees

In triangle AMB, we know that the sum of all measure of a triangle is 180 degrees and we have measure angle MAB = 29 degrees and measure angle MBA = 48 degrees
Therefore,
measure angle AMB = 180 - (29+48) = 103 degrees