Question

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)

Answer 1

Angle QOS= ANGLE QOR +ANGLE ROS
ANGLE ROS = ANGLE QOS - ANGLE QOR______(1)

ANGLE POR = ANGLE POS +ANGLE ROS
ANGLE ROS = ANGLE POR - ANGLE POS____(2)

(1) + (2)=
ANGLE ROS + ANGLE ROS = ANGLE QOS - ANGLE QOR + ANGLE POR - ANGLE POS
2 (ANGLE ROS) = ANGLE QOS - ANGLE POS [ANGLE QOR = ANGLE POR]
ANGLE ROS = 1/2 (ANGLE QOS - ANGLE POS)