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.
ABCD – rectangle;
point M – lies on the BC;
angle АMB = angle АМD;
AD = 2AB.
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
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