Question

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

Answer 1

Let $\angle A+\angle B=125°\text{and}\angle A+\angle C=113°$.
Then,
$$\begin{gathered} \angle A+\angle B+\angle A+\angle C=\left(125+113\right)° \\ \Rightarrow \left(\angle A+\angle B+\angle C\right)+\angle A=238° \\ \Rightarrow 180°+\angle A=238° \\ \Rightarrow \angle A=58° \end{gathered}$$

$\therefore \angle B=125°-\angle A$
$$\begin{gathered} =\left(125-58\right)° \\ =67° \end{gathered}$$

$\therefore \angle C=113°-\angle A$
$$\begin{gathered} =\left(113-58\right)° \\ =55° \end{gathered}$$