Question

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Answer 1

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Answer 2

Chapter # 6

Class - 9

(Lines & Angles)

Answer:

∠QRS = 60°

Explanation:

Correct Question:

In the given figure, if PQ || ST, ∠PQR = 110º and ∠RST = 130º, find ∠QRS.

Note: Figure is in Attachment.

Solution:

Given that,

PQ ║ST

We draw a line XY ║ST

So,

XY ║PQ, i.e PQ║ST║XY

Since,

PQ║XY & QR                         (They are transversal)

So,

∠PQR + ∠QRX = 180°

$\bigstar \sf Interior\;angles\;on\;the\;same\;side\;of\;the\;transversal\;are\;supplementry.\bigstar$

110°+∠QRX = 180°

∠QRX = 180° - 110°

∠QRX = 70°

Also,

ST║XY & SR                       (They are transversal)

∠SRY + ∠RST = 180°

$\bigstar \sf Interior\;angles\;on\;the\;same\;side\;of\;the\;transversal\;are\;supplementry.\bigstar$

130°+∠SRY = 180°

∠SRY = 180° - 130°

∠SRY = 50°

Since,

XY is a line.

∠QRX + ∠QRS + ∠SRY = 180°                          (Linear pair)

70°+∠QRS + 50° = 180°

120°+∠QRS = 180°

∠QRS = 180° - 120°

∠QRS = 60°

Hence,

The value of ∠QRS = 60°