In a triangle ABC, the angle B is a straight line, M is the intersection point of the bisectors of angles

In a triangle ABC, the angle B is a straight line, M is the intersection point of the bisectors of angles A and C. Determine the angle AMC.

The bisector of angle A divides angle A into two equal parts, let us denote half of angle A by the letter x, then angle A is equal to 2x.

The bisector of the angle C divides the angle C into two equal parts, we denote half of the angle C with the letter y, then the angle C is equal to 2y.

Since the sum of the angles in a triangle is 180 °, it turns out:

2x + 2y + 90 ° = 180 °.

2x + 2y = 180 – 90;

2 (x + y) = 90;

x + y = 90/2;

x + y = 45 °.

In triangle AMC: angle A is equal to x, angle C is equal to y.

x + y + (angle AMC) = 180 °.

AMC = 180 – (x + y).

Since x + y = 45, it turns out that the angle AMC = 180 – 45 = 135 °.

Answer: The AMC angle is 135 °.