Question

ABCD is a quadrilateral whose diagonals intersect each other at the point O such that a is equal to o b o b is equal to OD if angle abc is equal to 30 degree then the measure of angle b is equal to​

Answer 1

ANSWER

Given, OA=OB

∴∠OAB=∠OBA (opp. angle of equal side is equal)

Thus, ∠OAB=∠OBA=30

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In ΔOAB

∠OAB+∠AOB+∠OBA=180

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(Angle Sum Property)

30

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+∠AOB+30

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=180

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∠AOB=120

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As DOB is a straight line

∴∠DOA=180

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(Linear Pair)

∠DOA+∠AOB=180

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∠DOA=60

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Now, in ΔAOD

∠ODA+∠DOA+∠DAO180

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2∠ODA+60

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=180

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[∵∠ODA=∠DOAasOA=OD]

2∠ODA=120

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∠ODA=60

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Hence, option 'C' is correct.