Question

4. In Fig. 6.31, if PQ || ST, POR = 110° and
ZRST = 130°, find Z QRS.
[Hint : Draw a line parallel to ST through
point R.]

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Answer 1

Let us draw a line XY

parallel to ST and passing through point R.

∠PQR + ∠QRX

= 180º (Co-interior angles on the same side of transversal QR)

⇒ 110º +

∠QRX = 180º

⇒ ∠QRX =

70º

Also,

∠RST + ∠SRY

= 180º (Co-interior angles on the same side of transversal SR)

130º + ∠SRY

= 180º

∠SRY = 50º

XY is a straight line.

RQ and RS stand on it.

∴ ∠QRX +

∠QRS + ∠SRY

= 180º

70º + ∠QRS

+ 50º = 180º

∠QRS = 180º

− 120º = 60º

hope it helps

Answer 2

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