Question

In ∆PQR, if ∠P − ∠Q = 42° and ∠Q − ∠R = 21°, find ∠P, ∠Q and ∠R.

Answer 1

$\mathrm{Given}:\angle P-\angle Q=42°\text{and}\angle Q-\angle R=21°$
Then,
$$\begin{gathered} \angle P=42°+\angle Q\text{and}\angle R=\angle Q-21° \\ \therefore 42°+\angle Q+\angle Q+\angle Q-21°=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 3\angle Q=159° \\ \Rightarrow \angle Q=53° \end{gathered}$$

$\mathbf{\therefore }\angle P=42°+\angle Q$
$$\begin{gathered} =\left(42+53\right)° \\ =95° \end{gathered}$$

$\therefore \angle R=\angle Q-21°$
$$\begin{gathered} =\left(53-21\right)° \\ =32° \end{gathered}$$