Question

"Question 4 In the given figure, if PQ || ST, ∠PQR = 110º and ∠RST = 130º, find ∠QRS. [Hint: Draw a line parallel to ST through point R.]

Class 9 - Math - Lines and Angles Page 104"

Answer 1

Interior angles on the same side of the transversal:

 

The pair of interior angles on the same side of the transversal are called consecutive interior angles or allied angles or co interior angles.

 

If a transversal intersects two Parallel Lines then each pair of interior angles on the same side of the  transversal is supplementary.

 

 

If a transversal intersects two lines such that a pair of alternate interior angles is equal then the two lines are parallel.

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Given,

PQ || ST, ∠PQR = 110° and ∠RST = 130°

Construction,

A line XY parallel to PQ and ST is drawn.

 

∠PQR + ∠QRX = 180° (Angles on the same side of transversal.)
⇒ 110° + ∠QRX = 180°
⇒ ∠QRX = 70°
Also,
∠RST + ∠SRY = 180° (Angles on the same side of transversal.)
⇒ 130° + ∠SRY = 180°
⇒ ∠SRY = 50°
Now,
∠QRX +∠SRY + ∠QRS = 180°
⇒ 70° + 50° + ∠QRS = 180°
⇒ ∠QRS = 60°

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hope this will help you....

Answer 2

yes here is your answer
=> <RST+<SRU=180°
=> <SRU = 180° - 130° = 50---------(1)
<QRU,= <PQR= 110 [alternate angle]

=> <QRS+<SRU= 110°
=> <QRS+50°=110° ( from ( 1) )
=> <QRS = 110° - 50° = 60°