The bisectors of the angles n and m of the triangle mnr intersect at point a.

The bisectors of the angles n and m of the triangle mnr intersect at point a. find the angle to us if the angle is n = 84 degrees, and the angle is m = 42 degrees.

By condition, it is known that the angle H = 84 °. The bisector HА divided it in half, hence the angle MHA = 84 ° / 2 = 42 °.

Also, by condition, it is known that the angle M = 42 °. The MA bisector divided it in half, hence the angle HMA = 42 ° / 2 = 21 °.

It is known that the sum of the angles of any triangle is 180 °. Then, knowing the two angles of the triangle МАH, we can easily find the third angle that remains unknown.

Thus, the angle MAH = 180 ° – MHA – HMA;

MAH = 180 ° – 42 ° – 21 ° = 117 °.

Answer: angle MAH = 117 °.