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3 years ago

Given: Quadrilateral DEFG

Mathematics

1 answer:

nadya68 [22]3 years ago

3 0

We know that
The inscribed angle Theorem states that t<span>he inscribed angle measures half of the arc it comprises.
</span>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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