19. In the given figure PQ II ST, <POR 110Â°, and RST-130 find <QRS

1.	19. In the given figure PQ II ST, <POR 110Â°, and RST-130 find <QRS
Answer» Interior angles on the same side of thetransversal: The pair of interior angles on the same side ofthe transversal are called consecutive interior angles or allied angles or cointerior angles. If a transversal intersects two Parallel Linesthen each pair of interior angles on the same side of the transversal is supplementary. If a transversal intersects two lines such thata pair of alternate interior angles is equal then the two lines are parallel. 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° Like my answer if you find it useful!

Answer»

Interior angles on the same side of thetransversal:

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

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

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

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°

Like my answer if you find it useful!

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