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    Question

    ABCD is a cyclic quadrilateral and BC is a diameter of

    the circle. If ∠DBC = 29°, then ∠BAD = ?
    A 141⁰ Correct Answer Incorrect Answer
    B 138⁰ Correct Answer Incorrect Answer
    C 140⁰ Correct Answer Incorrect Answer
    D 119⁰ Correct Answer Incorrect Answer

    Solution

    According to the question ∠DBC = 29°  ∠BDC = 90°  [Angle in a semicircle is 90°] We know that sum of all the sides of triangles is 180°  ⇒ ∠DBC + ∠BDC + ∠BCD = 180°  ⇒ 29° + 90° + ∠BCD = 180°  ⇒ 119° + ∠BCD = 180°  ⇒ ∠BCD = (180° – 119°) ⇒ ∠BCD = 61°  Now, We know that, the opposite angles in a cyclic quadrilateral is 180°  So, ⇒ ∠BAD + ∠BCD = 180°  ⇒ ∠BAD + 61° = 180°  ⇒ ∠BAD = (180° – 61°) ⇒ ∠BAD = 119° 

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