In triangle MKP, the median MC = half of the side KP. Find the angle M of triangle MKP.

Let’s deal with this task.
Given:
MKP – triangle
MC is the median, which is half of the side of KP.
To find:
∠M =?
Decision:
MS = KS = RS
Since the MC is equal to half of the side of the KR (by condition)
MS = KS
From this it follows that the ISS is an isosceles triangle
∠СМК = ∠К = x
MS = RS
So MRS is an isosceles triangle
∠СМР = ∠Р = у
∠М = ∠СМР + ∠КМС = х + у
By the theorem on the sum of angles in a triangle MCS:
∠М + ∠К + ∠Р = 180 °
Hence, y + x + y + x = 180 °
2 (y + x) = 180 °
180: 2 = 90 ° = y + x = ∠M
Answer: Angle M is 90 °