Question
In the given figure, $\angle Q: \angle R = 1: 2.$ Find:$a. \angle Qb. \angle R$
✓
Answer
$\angle Q : \angle R = 1 : 2$
Let $\angle Q = x^\circ $
$\Rightarrow \angle R = 2x^\circ $
Now,$ \angle RPX = \angle Q + \angle R ....[$Exterior angle property$]$
$\Rightarrow 105^\circ = x^\circ + 2x^\circ $
$\Rightarrow 105^\circ = 3x^\circ $
$\Rightarrow x = 35^\circ $
$\Rightarrow \angle Q = x^\circ = 35^\circ $ and $\angle R = 2x^\circ = 70^\circ .$
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