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

Question:

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

Solution:

Given : $\angle P-\angle Q=42^{\circ}$ and $\angle Q-\angle R=21^{\circ}$

Then,

$\angle P=42^{\circ}+\angle Q$ and $\angle R=\angle Q-21^{\circ}$

$\therefore 42^{\circ}+\angle Q+\angle Q+\angle Q-21^{\circ}=180^{\circ} \quad[$ Sum of the angles of a triangle $]$

$\Rightarrow 3 \angle Q=159^{\circ}$

$\Rightarrow \angle Q=53^{\circ}$

$\therefore \angle P=42^{\circ}+\angle Q$

$=(42+53)^{\circ}$

$=95^{\circ}$

$\therefore \angle R=\angle Q-21^{\circ}$

$=32^{\circ}$