In ∆ABC, ∠A + ∠B = 125° and ∠A + ∠C = 113°. Find ∠A, ∠B and ∠C.

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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