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Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?

Quadrilateral CDEF is inscribed in circle A. Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _, which means that their measures are _. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE = 2 ⋅ m∠CDE. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.

central angles; equal to the measure of their intercepted arcs

inscribed angles; equal to the measure of their intercepted arcs

central angles; one half the measure of their intercepted arcs

inscribed angles; one half the measure of their intercepted arcs

"inscribed angles; one half the measure of their intercepted arcs" (Option D); and
inscribed angles; equal to the measure of their intercepted arcs (Option B).

It is to be noted that an intercepted arc is the arc that sits inside the inscribed angle. See the attached image.

Thus, it is correct to state that

The missing statements with regard to the mathematical proof are:

"inscribed angles; one half the measure of their intercepted arcs" (Option D); and
inscribed angles; equal to the measure of their intercepted arcs (Option B).

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