Given: Quadrilateral DEFG is inscribed in circle P.

Prove: m∠D+m∠F=180∘

A circle with point P at the center of the circle and quadrilateral D E F G is inscribed in the circle.



Drag and drop an answer to each box to correctly complete the proof.

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It is given that quadrilateral DEFG is inscribed in circle P. Because a circle measures 360°, mEFG+mGDE=360∘. By the __________, 12mEFG+12mGDE=180∘. By the inscribed angles theorem, __________ = 12mGDE and _________ = 12mEFG. This means m∠D+m∠F=180∘ by the ________.

(first picture is graph and second is the choices)