Question 4. in Fig. 6.31, If Pq || St, ? Pqr = 110° and ? Rst = 1 Exercise 6.2 Chapter 6 Lines and Angles Maths Class

Question 4. In Fig. 6.31, if PQ || ST, ? PQR = 110° and ? RST = 130°, find ? QRS. Chapter 6: Lines and Angles Maths Class 9 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. Question 4. In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS. is solved by our expert teachers. You can get ncert solutions and notes for class 9 chapter 6 absolutely free. NCERT Solutions for class 9 Maths Chapter 6: Lines and Angles is very essencial for getting good marks in CBSE Board examinations

Question 4. In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.
[Hint : Draw a line parallel to ST through point R.]

Solution: Let us draw a parallel line XY to PQ || ST and passing through point R.
Sum of interior angle on the same side of the transversal is always = 180°

So that
∠ PQR + ∠ QRX = 180°
Given that ∠ PQR= 110°
110° + ∠QRX = 180°
∠QRX = 180° -110°
∠QRX = 70°
Sum of interior angle on the same side of the transversal is always = 180°

∠RST + ∠SRY = 180° (Co-interior angles on the same side of transversal SR)
Also
130° + ∠SRY = 180°
∠SRY = 50°
XY is a straight line. Use property of linear pair we get
∠QRX + ∠QRS + ∠SRY = 180°
70° + ∠QRS + 50° = 180°
∠QRS = 180° − 120°
= 60°