Quadrilateral bird is inscribed in circle o. what is the measure of angle d?

    ∠D = 63°

Step-by-step explanation:

Because all four corners of the quadrilateral rest on the circumference of the circle, then BIRD is a cyclic quadrilateral (circle theorem).

According to circle theorem, opposite angles of a cyclic quadrilateral are supplementary (sum to 180°).

∴  ∠I + ∠D = 180°

       ⇒ ∠D = 180° - ∠I

       ⇒ ∠D = 180° - 117°  (since ∡I = 117°)

        ∴ ∠D = 63°

560

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