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Question

ABCD is parallelogram. The angle bisectors of ∠A and ∠D intersect at O. Find the measures of ∠AOD.

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Solution


In parallelogram ABCD,A+D=180° Adjacent angles of a parallelogram are supplementary12A+12D=180°2OAD+ODA=90° .....i As, OA and OD are angle bisectors of A and D, respectivelyNow, in AOD,AOD+OAD+ODA=180° Angle sum property of triangleAOD+90°=180° Using iAOD=180°-90° AOD=90°


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