ABCD is a parallelogram. The angle bisectors of ∠Aand∠D meet at O. Find the measure of ∠AOD.
A
120∘
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B
35∘
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C
40∘
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D
90∘
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Solution
The correct option is D90∘
Let ∠BAD=x∘ ⇒∠ADC=180∘−x∘ [Sum of adjacent angles of a parallelogram is 180∘] ∴∠BAD2=x2=∠OAD and ∠ADC2=90−x2=∠ADO [AO and DO are angle bisectors] ∴∠AOD=180−(x2+90−x2)=90∘