Question

In figure POQ is a line. Raw Oris perpendicular to line PQ .OS is another ray lying between rays OP and OR. Prove that `angleROS(1)/(2) (angleQOS-anglePOS)i.e., angle1=(1)/(2)(angle2-angle3)`

Answer 1

Since, Oris perpendicular to PQ
`:. angle1+angle3=angle4`
Now, `angle1=angle2-angle4 " " ("each" 90^(@)) .....(1)`
`rArrangle1=angle2-(angle1+angle3)" "` (from the figure)
`rArr angle1= angle2-angle1-angle3 " "` [ from (1)]
`rArr 2angle1=angle2-angle3`
`rArrangle1=(1)/(2)(angle2-angle3)`