In rectangle ABCD, the bisector of angle A intersects side BC at point M. Find angle AMB.

Given:
rectangle ABCD,
AM is the bisector of angle A,
point M belongs to the BC side.
Find the degree measure of the angle AMB -?
Decision:
1. Consider the rectangle ABCD. It has all angles of 90 degrees, that is, angle A = angle B = angle C = angle D = 90 degrees.
2. Consider a right-angled triangle ABM. Since AM is a bisector, the angle BAM = 90: 2 = 45 (degrees). Knowing that the sum of the degree measures of the angles of the triangle is 180 degrees, we get:
angle AMB = 180 – angle BAM – angle ABM;
angle AMB = 180 – 45 – 90;
angle AMB = 45 degrees.
Answer: 45 degrees.