Question

PC
In the adjacent figure PQ || ST, POR
110 and ZRST-130°, find ZQRS.
(Hint: Draw a line parallel to ST through
point R.)
1100​

Answer 1

Step-by-step explanation:

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