class IX NCERT Lines and Angles

LINES AND ANGLES

1. In Fig. ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠ POS and ∠ SOQ, respectively. If ∠ POS = x, find ∠ ROT. 

2. In Fig. , if x + y = w + z, then prove that AOB is a line. 

3. In Fig. , POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ ROS = 1/ 2 (∠ QOS – ∠ POS). 

4. It is given that ∠ XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ ZYP, find ∠ XYQ and reflex ∠ QYP.

5. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

6.  In Fig., if AB || CD, EF ⊥ CD and ∠ GED = 126°, find ∠ AGE, ∠ GEF and ∠ FGE.

 4. In Fig, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.  

5. In Fig., if AB || CD, ∠ APQ = 50° and ∠ PRD = 127°, find x and y. 

6. In Fig, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.

7. In Fig, the sides AB and AC of ∆ABC are produced to points E and D respectively. If bisectors BO and CO of ∠ CBE and ∠ BCD respectively meet at point O, then prove that ∠ BOC = 90° – 1/ 2 ∠BAC.

8. In Fig. , the side QR of ∆ PQR is produced to a point S. If the bisectors of ∠ PQR and ∠ PRS meet at point T, then prove that ∠ QTR = 1/ 2 ∠ QPR.

9. In Fig. , if PQ ⊥ PS, PQ || SR, ∠ SQR = 28° and ∠ QRT = 65°, then find the values of x and y.