Given $∠ P O R = 3 x$ and $∠ Q O R = (2 x + 10) °$ . If POQ is a straight line then, the value of $∠ P O R$ is ______.

99°

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100°

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102°

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103°

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Solution

The correct option is C 102°

Given, POQ is a srtaight line.

$∠ P O R + ∠ Q O R = 180 °$ .... (Linear pair)
$(3 x) ° + (2 x + 10) ° = 180 °$
$\Rightarrow 5 x + 10 ° = 180 °$
$\Rightarrow 5 x = 180 ° - 10 ° = 170 °$
$\Rightarrow 5 x = 170 °$
$\Rightarrow x = \frac{170 °}{5} = 34 °$

The value of $∠ P O R = (3 x) ° = (3 \times 34) ° = 102 ° .$

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