Question

if PQ parallel to ST,angle PQR=110 and angle RST=130,
find angle QRS​

Answer 1

Answer:

Step-by-step explanation:

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°

Hope it helps..

Answer 2

Answer:

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 = 180° - 110°

∠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°

Hence, ∠QRS = 60°