Here's the question you clicked on:
madhukumari2626
in triangle ABC BD is perpendicularAC and CE perpendicular AB if BD and CE intersect at O prove that angle BOC = 180 _BAC
opposite sides of a quadrilateral are supplementary
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this is what is missing |dw:1374652805954:dw| Angle OEA and Angle ODA are both 90 so they sum to 180. by angle sum of a quadrilateral EAD + EOD = 180 or are supplementary
the quadrilateral is DOEA so EAD + EOD = 360 - 180
the fact they are perpendicular are given to you in the question
And that makes EAD + EOD = 180, as Krishnadas posted.
yep... the initial statement about opposite sides being supplementary makes no sense. by if you show the right angles on the perpendiculars then it makes it easy to understand that EAD and EOD are supplementary