ABCD is a quadrilateral in which angle BAD =105, angel BCD =150 and BC= 13cm . find AC? please solve this question​

Question

ABCD is a quadrilateral in which angle BAD =105, angel BCD =150 and BC= 13cm . find AC? please solve this question​

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Claire 1 month 2021-08-16T03:29:33+00:00 1 Answers 0 views 0

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    2021-08-16T03:30:36+00:00

    Answer:

    (i) Join BD

    Now, ABCD is a cyclic quadrilateral

    ∴ ∠BAD + ∠BCD = 180° (Opposite angles of a cyclic quadrilateral)

    => ∠BAD + 150° = 180°

    => ∠BAD = 180° – 150° = 30°

    (ii) ∠ABD = 90° (Angle in a semi-circle)

    Now, In △ABD, we have

    ∠ABD + ∠BAD + ∠ADB = 180°

    90° + 30° + ∠ADB = 180°

    => ∠ADB = 180° – 120° = 60°

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