Mathematics

# In $\triangle ABC$, if $\angle A + \angle B = 125^{\circ}$ and $\angle A + \angle C = 113^{\circ}$, find $\angle A, \angle B$ and $\angle C$.

##### SOLUTION
It is given that $\angle A + \angle B = 125^{\circ} \dots (1)$

We know that the sum of all the angles in a triangle is $180^{\circ}$.

So we can write it as

$\angle A + \angle B + \angle C = 180^{\circ}$

By substituting $\angle A + \angle B = 125^{\circ}$ in the above equation

$125^{\circ} + \angle C = 180^{\circ}$

On further calculation

$\angle C = 180^{\circ} - 125^{\circ}$

By subtraction

$\angle C = 55^{\circ}$

It is given that $\angle A + \angle C = 113^{\circ}$

By substituting the value of $\angle C$

$\angle A + 55^{\circ} = 113^{\circ}$

On further calculation

$\angle A = 113^{\circ} - 55^{\circ}$

By subtraction

$\angle A = 58^{\circ}$

By substituting $\angle A = 58^{\circ}$ in equation (1)

So we get

$\angle A + \angle B = 125^{\circ}$

$58^{\circ} + \angle B= 125^{\circ}$

On further calculation

$\angle B = 125^{\circ} - 58^{\circ}$

By subtraction

$\angle B = 67^{\circ}$

Therefore, $\angle A = 58^{\circ}, \angle B = 67^{\circ}$ and $\angle C = 55^{\circ}$.

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
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