Calculate Angle MAB in a Right Triangle with 50° Base Angle

Question

ΔABC is a right triangle.

$∢\text{ABC}=50$

Calculate the size of angle $∢\text{MAB}$ .

Since we are given that AM bisects BC, we can claim that AM is a median, therefore:

$AM=BM=MC$

As a result, we have created an isosceles triangle BMA, where $BM=MA$

Since we are given that angle B is equal to 50, and in an isosceles triangle the base angles are equal to each other, we can claim:

$B=MAB=50$