Cis the center of the circle.

in order to prove that opposite angles of a quadrilateral inscribed in a circle are supplementary (in this case m∠edg + m∠efg = 180°), which fact is most important to know?

Option D is correct.

Step-by-step explanation:

Given C is the center of the circle.

we have to prove opposite angles of a quadrilateral inscribed in a circle are supplementary.

By the theorem, the angle subtended by an arc at the center is double the angle subtended at any point on the circumference of a circle.

i.e

Hence, the fact which is used to prove the above is

i.e option D is used.