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

Asked by umang agrawal | 16th Sep, 2010, 12:00: AM

Expert Answer:

Dear Student,
 
Refer the figure given below,
 
 
 
from the figure, we have
 
QOS + POS = 180     --------- (1)
 
Also,
QOS  - ROS = 90
 
=> 2x(QOS - ROS) = 180     -------- (2)
 
From (1) and (2), we get
 
QOS + POS  = 2xQOS - 2xROS
 
=> 2xROS = QOS - POS
 
=> ROS = (QOS - POS)/2
 
Hence proved.
 
Regards Topperlearning.

Answered by  | 16th Sep, 2010, 10:35: PM

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