Question

In the adjacent figure PQ || ST, ∠PQR=110° and ∠RST=130°, find ∠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°

HOPE THIS WILL HELP YOU..

Answer 2

Hi ,

Given PQ//ST

Draw a line ' l ' parallel to ST through R .

From the figure

a + 110° = 180°

And

c + 130° = 180°

[ Interior angles on the same side of the

transversal ]

a = 180° - 110° = 70°

c ,= 180° - 130° = 50°

Also

a + b + c = 180°

[ Angles at a point on a line ]

70° + b + 50° = 180°

b = 180° - 70° - 50°

b = 60°

Therefore ,

<QRS = 60°

I hope this helps you.

: )