Question

In the given figure PQ//ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS. [Hint : Draw a line parallel to ST through point R.]

Answer 1

Given PQ // ST 

Draw a lipe ‘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° – 120° = 60° 

∴ ∠QRS = 60°