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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)` |
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Answer» 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)` |
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