Point M is selected inside the square ABCD, so that the equilateral triangle AMD find the angle AMB.
| April 5, 2021 | education
Since the triangle ADM, by condition, is equilateral, then AB = AM = DM, and the inner angles of the triangle are 60.
Then in the triangle ABM the angle BAM = (90 – MAD) = (90 – 60) = 30.
Since AM = AD, and AD = AB, as the sides of the square, AB = AM, and therefore the triangle ABM is isosceles. Then the angle ABM = AMB = (180 – BAM) / 2 = (180 – 30) / 2 = 150/2 = 75.
Answer: Angle AMB is 75.
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