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Quadrilaterals Test - 10

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  • Question 1
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    The Diagonals AC and BD of a Parallelogram ABCD intersect each other at the point O such that ∠DAC = 30∘ and ∠AOB = 70. Then, ∠DBC ?

    Solution

    angle DAC = angle ACB = 30 ( alternate angles)

    angle BOA + angle BOC = 180 ( linear pair)

    angle BOC = 180 - 70 = 110

    In triangle BOC, angle BOC + angle OCB + angle CBO = 180 ( angle sum property)

    110 + 30 + angle CBO = 180

    angle CBO = 180 - 140 =40 = angle DBC

     

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