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

ΔABC is a right triangle.

∢ABC=50 ∢\text{ABC}=50

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

AAABBBCCCMMM50

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

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1

Understand the problem

ΔABC is a right triangle.

∢ABC=50 ∢\text{ABC}=50

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

AAABBBCCCMMM50

2

Step-by-step solution

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

AM=BM=MC AM=BM=MC

As a result, we have created an isosceles triangle BMA, where BM=MA 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 B=MAB=50

3

Final Answer

50

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Indicates which angle is greater

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