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

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

Line AM intersects parallel lines AD and BC, which means the angles AMB and MAD are crosswise and equal.

Accordingly, triangle АМD is isosceles (АD = МD). The angles АМD and МАD are equal to each other and let them be equal to X.

Consider a triangle MCD. It is rectangular, the leg DC = AB and 2 times less than the hypotenuse MD, which is equal to AD. The DMC angle is 180 – 2X and lies against the leg, which is 2 times less than the hypotenuse, which means the DMC angle is 30. Whence, the AMB angle = AMD angle = (180 – 30) / 2 = 75.