In an isosceles triangle ABC, AC = BC, the angle is C = 80, AM is the bisector of the triangle. Find the angle AMB-?

univerkov | April 26, 2021 | education

1. Since AC = BC; AB is the base;

∠ A = ∠ B, we find their value:

∠A + ∠B + ∠C = 180;

∠A = ∠B = (180 – 80): 2 = 50.

2. AM is the bisector of ∠A, we find ∠MAB:

∠MAB = ∠A: 2 = 25.

3. Consider the triangle AMB:

∠MAB = 25;

∠B = 50;

Find the angle ∠AMB = 180 – 50 – 25 = 105.

Answer: 105.

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