Harshit Singh
Last Activity: 4 Years ago
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.