The median CM is drawn in the right-angled triangle ABC (медиC = 90 °). Find the degree measure ∠AMC if ∠CBA = 20 °.

The median is the segment dividing the opposite side in half.

Since the median drawn from the vertex of the right angle is equal to half of the hypotenuse, we get 2 isosceles triangles: AMC (AM = MC) and CMB (CM = MB).

In triangle AMC, the angles CAM and ACM are equal. Their degree measure is equal to:

90 ° – 20 ° = 70 °.

Then the AMC angle will be equal to:

180 ° – 70 ° * 2 = 180 ° – 140 ° = 40 °.