You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Angle Sum Property

In the fig, i...

Question

In the fig, if the lines $P Q$ and $R S$ intersect at point $T$ such that $∠ P R T = 40^{o}, ∠ R P T = 92^{o}$ and $∠ T S Q = 70^{o}$ find $∠ S Q T$ (in degrees).

Open in App

Solution

In $△ P R T,$
$∠ P R T + ∠ R T P + ∠ R P T = 180^{o}$
$40^{o} + 92^{o} + ∠ R T P = 180^{o}$
$\Rightarrow ∠ R T P = 48^{o}$
In $△ P R T$ and $△ T S Q$ ,
$∠ P T R = ∠ S T Q = 48^{\circ}$ (Vertically opposite angles)
In $△ S T Q,$
$∠ S T Q + ∠ S Q T + ∠ T Q S = 180^{o}$
$48^{o} + 70^{o} + ∠ S Q T = 180^{o}$
$∠ S Q T = 62^{o}$

Suggest Corrections

Similar questions

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

∠ P R T = 40^{o}, ∠ R P T = 95^{o}

and

∠ T S Q = 75^{o}

, find

∠ S Q T

Q. In the given figure if line segments

P Q

and

R S

intersect at point

T

, such that

∠ P R T = 40^{o}, ∠ R P T = 95^{o}

and

∠ T S Q = 75^{o}

, find

∠ S Q T

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 $∠ S Q T$ .

Q. In the fig 2.58, if the lines PQ and RS intersect at Point T such that

∠

PRT = 40

°

∠

RPT = 92

°

and

∠

TSQ = 70

°

find

∠

SQT.

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

Join BYJU'S Learning Program

In the fig, if the lines PQ and RS intersect at point T such that ∠PRT=40o,∠RPT=92o and ∠TSQ=70o find ∠SQT (in degrees).

In △PRT,∠PRT+∠RTP+∠RPT=180o40o+92o+∠RTP=180o⇒∠RTP=48oIn △PRT and △TSQ,∠PTR=∠STQ=48∘ (Vertically opposite angles)In △STQ,∠STQ+∠SQT+∠TQS=180o48o+70o+∠SQT=180o∠SQT=62o

In the fig, if the lines $P Q$ and $R S$ intersect at point $T$ such that $∠ P R T = 40^{o}, ∠ R P T = 92^{o}$ and $∠ T S Q = 70^{o}$ find $∠ S Q T$ (in degrees).