Question

In △ ABC, if ∠A + ∠B = 125° and ∠A + ∠C = 113°, find ∠A, ∠B and ∠C.

Answer 1

It is given that ∠A + ∠B = 125^o …. (1)

We know that the sum of all the angles in a triangle is 180^o.

So we can write it as

∠A + ∠B + ∠C = 180^o

By substituting ∠A + ∠B = 125^o in the above equation

125^o + ∠C = 180^o

On further calculation

∠C = 180^o – 125^o

By subtraction

∠C = 55^o

It is given that ∠A + ∠C = 113^o

By substituting the value of ∠C

∠A + 55^o = 113^o

On further calculation

∠A = 113^o – 55^o

By subtraction

∠A = 58^o

By substituting ∠A = 58^o in equation (1)

So we get

∠A + ∠B = 125^o

58^o + ∠B= 125^o

On further calculation

∠B = 125^o – 58^o

By subtraction

∠B = 67^o

Therefore, ∠A = 58^o, ∠B = 67^o and ∠C = 55^o