Question

In ∆ABC, if ∠A − ∠B = 40° and ∠B − ∠C = 10°, find the measures of ∠A, ∠B and ∠C.

Answer 1

$$\begin{gathered} \angle A-\angle B=40°...\left(i\right) \\ \angle B-\angle C=10°...\left(ii\right) \\ \mathrm{From}\left(i\right),\text{we have:} \\ \angle B=\angle A-40°...\left(iii\right) \\ \mathrm{Adding}\left(i\right)\mathrm{and}\left(ii\right),\text{we get:} \\ \angle A-\angle C=50° \\ \Rightarrow \angle C=\angle A-50°...\left(iv\right) \end{gathered}$$
Now,
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow \angle A+\angle A-40°+\angle A-50°=180°\left[\text{Using}\left(iii\right)\text{and}\left(iv\right)\right] \\ \Rightarrow 3\angle A=270° \\ \Rightarrow \angle A=90° \\ \therefore \angle B=90°-40°=50°\text{and} \\ \angle C=90°-50°=40° \end{gathered}$$