Given $∠ P O R = 3 x$ and $∠ Q O R = 2 x + 10^{\circ}$ , find the value of x for which POQ will be a line.

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Solution

$∠ P O R = 3 x a n d ∠ Q O R = 2 x + 10^{\circ}$
If POQ is a line, then
$∠ P O R + ∠ Q O R = 180^{\circ}$ (Linear pair)
$\Rightarrow 3 x + 2 x + 10^{\circ} = 180^{\circ} \Rightarrow 5 x = 180^{\circ} - 10^{\circ} = 170^{\circ} \Rightarrow x = \frac{170^{\circ}}{5} = 34^{\circ} ∴ x = 34^{\circ}$

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