Question

If PQ|| ST, $\angle PQR={110}^o$ and $\angle RST={130}^o$, find $\angle QRS$.
[Hint : Draw a line parallel to ST through point R.]

Answer 1

Interior angles on the same side of the transversal:The pair of interior angles on the same side of the transversal are called consecutive interior angles or allied angles or co interior angles.

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

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

SOLUTION :

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°