Question
In figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint. Draw a line parallel to ST through point R.]
Solution
Construction: Draw a line RU parallel to ST through point R.
∠RST + ∠SRU = 180°
| Sum of the consecutive interior angles on the same side of the transversal is 180°
⇒ 130° + ∠SRU = 180°
⇒ ∠SRU = 180° - 130° = 50° ...(1)
∠QRU = ∠PQR = 110°
| Alternate Interior Angles
⇒ ∠QRS + ∠SRU = 110°
⇒ ∠QRS + 50° = 110° | Using (1)
⇒ ∠QRS = 110° - 50° = 60°.
