Abcd is a parallelogram. the bisector of ∠a and ∠d meet at o. what is the measure of ∠aod? sol: abcd is a parallelogram with ab∥cd and bc∥ad.ao and do are bisectors of ∠dab and ∠adc respectively.
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angle A + angle D = 180 (adjacent angles of a parallelogram)
implies (1/2)(angle A + angle D) = 90
implies angle OAD + angle ODA =90 (OD and OA are angle bisectors)
Now in ∆OAD , applying angle sum property we have
angle OAD + angle ODA + angle DOA = 180
90 + angle DOA = 180
implies angle DOA = 90
or angle O = 90
implies (1/2)(angle A + angle D) = 90
implies angle OAD + angle ODA =90 (OD and OA are angle bisectors)
Now in ∆OAD , applying angle sum property we have
angle OAD + angle ODA + angle DOA = 180
90 + angle DOA = 180
implies angle DOA = 90
or angle O = 90
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