If lines PQ and RS intersect at point T- such that - PRT - 40 - - RPT - 95 - and - TSO - 75 - - find - SQT-

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Standard IX

Mathematics

Quadrilaterals

If lines PQ a...

Question

If lines PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}$ , $∠ R P T = 95^{\circ}$ and $∠ T S O = 75^{\circ}$ , find $∠ S Q T$ .

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Solution

Find $∠ S Q T$

In $△ P R T$

$∠ R P T + ∠ P R T + ∠ R T P = 180^{o}$

$95 + 40 + ∠ R P T = 180^{o}$

$∠ R T P = 45^{o}$

$∠ Q T S = ∠ R T P$ (vertically opposite angle )

$∠ Q T S = 45^{o}$

In $△ S T Q$

$∠ T S Q + ∠ S T Q + ∠ S Q T = 180^{o}$

$45^{o} + 75^{o} + ∠ S Q T = 180^{o}$

$∠ S Q T = 60^{o}$

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In fig, if line PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}$ , $∠ R P T = 95^{\circ}$ and $∠ T S Q = 75^{\circ}$ , find $∠ S Q T$ .

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∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ}

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In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º, ∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.

Q. Question 4
In the given figure, if lines PQ and RS intersect at point T, such that

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Q. In the given figure if line segment

P Q

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If lines PQ and RS intersect at point T, such that ∠PRT=40∘, ∠RPT=95∘ and ∠TSO=75∘ , find ∠SQT.

Find ∠SQTIn △PRT∠RPT+∠PRT+∠RTP=180o95+40+∠RPT=180o∠RTP=45o∠QTS=∠RTP (vertically opposite angle )∠QTS=45oIn △STQ∠TSQ+∠STQ+∠SQT=180o45o+75o+∠SQT=180o∠SQT=60o

If lines PQ and RS intersect at point T, such that $∠ P R T = 40^{\circ}$ , $∠ R P T = 95^{\circ}$ and $∠ T S O = 75^{\circ}$ , find $∠ S Q T$ .