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    Question

    A triangle ABC is inscribed in a circle. The tangent at

    A meets the extended sides BC and AB at points P and Q, respectively. If ∠ACB = 30° and ∠BCA = 60°, find ∠PAQ. 
    A 90° Correct Answer Incorrect Answer
    B 120° Correct Answer Incorrect Answer
    C 150° Correct Answer Incorrect Answer
    D 180° Correct Answer Incorrect Answer

    Solution

    Since ∠ACB and ∠BCA are given,  the angle subtended by the arc AB at P (∠PAQ) is supplementary to ∠ACB (by the tangent-secant angle theorem),  so ∠PAQ = 180° - ∠ACB = 180° - 30° = 150°. Correct answer: c) 150°

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