In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that `angle ROS=1/2 (angle QOS-angle POS)`.

In Fig. 6.15, angle PQR = angle PRQ , then prove that angle PQS = angle PRT .

In Fig. 6.10, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of angle POS and angle SOQ , respectively. If angle POS = x , find angle ROT .

In Fig. 6.11, OP, OQ, OR and OS are four rays. Prove that angle POQ + angle QOR + angle SOR + angle POS = 360^@ .

In fig. angleABC=angleACB and angle3=angle4 . Prove that angle1=angle2

In Fig. 6.44, the side QR of triangle PQR is produced to a point S. If the bisectors of angle PQR and angle PRS meet at point T, then prove that angle QTR =1/2 angle QPR .

In Fig. 6.9, lines PQ and RS intersect each other at point O. If angle POR : angle ROQ = 5 : 7 , find all the angles.

In the fig. RT=TS, angle1=2angle2 and angle4=2angle3 . Prove that triangleRBTequivtriangleSAT