Lines PQ and RS intersect at O- If - POR - - ROQ -5- 7- Then - P OS -A- 105-B- 75-C- 45-

The correct option is A 105^∘ ∠ POR+∠ ROQ =180^∘(linear pair) and given nbsp;∠ POR:∠ ROQ = 5:7 Therefore nbsp;∠ POR = 5/12× 180 = 75^∘ and nbsp;∠ ROQ = 7 ...

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Byju's Answer

Standard IX

Mathematics

Vertically Opposite Angles

Lines PQ and ...

Question

Lines PQ and RS intersect at O. If $∠ P O R : ∠ R O Q = 5 : 7$ . Then $∠ P O S$ =

105^{\circ}

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75^{\circ}

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45^{\circ}

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Solution

The correct option is A $105^{\circ}$

$∠ P O R + ∠ R O Q = 180^{\circ}$ (linear pair) and given $∠ P O R : ∠ R O Q$ = 5:7

Therefore $∠ P O R = \frac{5}{12} \times 180 = 75^{\circ}$
and $∠ R O Q = \frac{7}{12} \times 180 = 105^{\circ}$

$∠ P O S = ∠ R O Q$ (vertically opposite angles)
$\to ∠ P O S = 105^{\circ}$

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Lines PQ and RS intersect at O. If∠POR:∠ROQ=5:7. Then ∠POS =

The correct option is A 105∘ ∠POR+∠ROQ=180∘(linear pair) and given ∠POR:∠ROQ = 5:7 Therefore ∠POR=512×180=75∘ and ∠ROQ=712×180=105∘ ∠POS=∠ROQ(vertically opposite angles) →∠POS=105∘

Lines PQ and RS intersect at O. If $∠ P O R : ∠ R O Q = 5 : 7$ . Then $∠ P O S$ =