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 $∢\text{MAB}$ .

00:00 Find MAB

00:07 Sum of angles in a triangle equals 180

00:17 Collect terms and isolate C

00:34 This is angle A

00:42 Median according to the given

00:49 The median to the hypotenuse equals half the hypotenuse

00:59 In an isosceles triangle, base angles are equal

01:09 Part of the angle equals the whole angle minus the second part

01:16 And this is the solution to the question

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:

$B=MAB=50$