Question

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.

Answer 1

The answer is down below.

Explanation:

I took the quiz. I hope this helps :)

Answer 2

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