Given: Quadrilateral DEFG is inscribed in circle P. Prove: m∠D+m∠F=180∘ Drag and drop an answer to each box to correctly complet
e the proof.
1 answer:
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
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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