Point M is taken in rectangle ABCD on the BC side so that the angle АМВ is equal to the angle АМD.

Point M is taken in rectangle ABCD on the BC side so that the angle АМВ is equal to the angle АМD. Find these angles if AD = 2AB.

Given:

ABCD – rectangle;

point M – lies on the BC;

angle АMB = angle АМD;

AD = 2AB.

To find:

corner AMB

corner AMD

Decision:

1) Consider the triangle ABM, since the angle B = 90 degrees, we find the angle A and the angle M.

Angle A = 1/2 (180 degrees – 90 degrees) = 45 degrees => Angle M is also 45 degrees.

2) If the angle АMB = angle AMD (by condition), then the angle AMD = 45 degrees.

Answer: Angle AMB = Angle AMD = 45 degrees