Question

In ∆ABC, if ∠A + ∠B = 125° and ∠A + ∠C = 113°, then ∠A = ?
(a) (62.5)°
(b) (56.5)°
(c) 58°
(d) 63°

Answer 1

(c) 58°

Let
$$\begin{gathered} \angle A+\angle B=125°...\left(i\right)\text{and} \\ \angle A+\angle C=113°...\left(ii\right) \end{gathered}$$
$$\begin{gathered} \mathrm{Adding}\left(i\right)\mathrm{and}\left(ii\right),\text{we get:} \\ \angle A+\angle A+\angle B+\angle C=\left(125+113\right)° \\ \Rightarrow \angle A+\left(\angle A+\angle B+\angle C\right)=238°\left[\because \left(\angle A+\angle B+\angle C\right)=180°\right] \\ \Rightarrow \angle A+180°=238° \\ \Rightarrow \angle A=\mathbf{58}\mathbf{°} \end{gathered}$$