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


Given: POQ is a straight line
OR ? PQ
OS lie between OP and OR
Construction: Draw OT between OR and OQ
Such that ?ROS = ?ROT
? 90° – ?ROS = 90° – ?ROT
? ?SOP = ?TOQ
Now
? ?SOT = ?SOQ – ?TOQ
? 2 ?ROS = ?QOS – ?POS
?ROS = 1/2(?QOS – ?POS)