Inside square ABCD, point M is selected so that triangle AMD is equilateral. Find angle AMB.
| September 5, 2021 | education
Since, by condition, the ADM triangle is equilateral, then all its internal angles are equal to 60.
Angle DAM = 60, then angle BAM = (90 – DAM) = (90 – 60) = 30.
Since AM = AD, and ABCD is a square, then AB = AM, and therefore the triangle ABM is isosceles, then the angle ABM = AMB = (180 – BAM) / 2 = (180 – 30) / 2 = 150/2 = 750.
Answer: Angle AMB is 750.
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