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

Byju's Answer

Standard IX

Mathematics

Linear Pair

In the fig 2....

Question

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.

Open in App

Solution

$In △ PRT, we have : ∠ P + ∠ R + ∠ T = 180 ° \Rightarrow 92 ° + 40 ° + ∠ T = 180 ° \Rightarrow ∠ T = 48 ° ∠ RTP = ∠ STQ = 48 ° (Vertically opposite angles) In △ STQ, we have : ∠ T + ∠ S + ∠ Q = 180 ° \Rightarrow 48 ° + 70 ° + ∠ Q = 180 ° \Rightarrow ∠ Q = 62 ° Thus, ∠ SQT = 62 °$

Suggest Corrections

Similar questions

Q. In the figure, if lines

P Q

and

R S

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

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, 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).

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

∠ P R T = 40^{\circ}, ∠ R P T = 95^{\circ} a n d ∠ T S Q = 75^{\circ}

, find

∠ S Q T .

Join BYJU'S Learning Program

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 △PRT, we have:∠P+∠R+∠T = 180°⇒92°+40°+∠T = 180°⇒∠T = 48°∠RTP=∠STQ=48° (Vertically opposite angles)In △STQ, we have:∠T+∠S+∠Q =180°⇒48°+70°+∠Q =180°⇒∠Q = 62°Thus, ∠SQT = 62°

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.