In triangle ABC BM is the median and BH is the height. It is known that AC = 64, HC = 16, and ∠ACB = 37 °. Find the angle AMB.

Since BM is the median, it means AM = MC = AC / 2 = 64/2 = 32
Consider the MBC triangle.
MH = MC-HC = 32-16 = 16, i.e. it turns out that MC = HC.
BH for this triangle is not only the height, but also the median. This is a property of an isosceles triangle.
By the property of an isosceles triangle: ∠BMC = ∠ACB = 37 °.
∠AMB = 180 ° -∠BMC = 180 ° -37 ° = 143 ° (as it is adjacent)
Answer: 143

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