In the adjacent figure pq ll st ,angle pqr=110and angle rst=130 ,find angle qrs.

Dear Student
Here is the 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°

the required theoretical knowledge is as follows:
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 thetransversal is supplementary.

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