Question:
In ∆ABC, ∠A + ∠B = 125° and ∠A + ∠C = 113°. Find ∠A, ∠B and ∠C.
Solution:
Let $\angle A+\angle B=125^{\circ}$ and $\angle A+\angle C=113^{\circ}$.
Then,
$\angle A+\angle B+\angle A+\angle C=(125+113)^{\circ}$
$\Rightarrow(\angle A+\angle B+\angle C)+\angle A=238^{\circ}$
$\Rightarrow 180^{\circ}+\angle A=238^{\circ}$
$\Rightarrow \angle A=58^{\circ}$
$\therefore \angle B=125^{\circ}-\angle A$
$=(125-58)^{\circ}$
$=67^{\circ}$
$\therefore \angle C=113^{\circ}-\angle A$
$=(113-58)^{\circ}$
$=55^{\circ}$
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