Given: quadrilateral defg is inscribed in circle p. prove: m∠d+m∠f=180∘ drag and drop an answer to each box to correctly complete the proof.

We know that
The inscribed angle Theorem states that the inscribed angle measures half of the arc it comprises.
so
m∠D=(1/2)*[arc EFG]
and
 m∠F=(1/2)*[arc GDE]

arc EFG+arc GDE=360°-------> full circle

applying multiplication property of equality
(1/2)*arc EFG+(1/2)*arc GDE=180°

applying substitution property of equality
m∠D=(1/2)*[arc EFG]
m∠F=(1/2)*[arc GDE]
(1/2)*arc EFG+(1/2)*arc GDE=180°----> m∠D+m∠F=180°

the answer in the attached figure

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