Use the diagram shown. Find EG.
B
E
37
75
23
F
A

C) one half the measure of their intercepted arcs; m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE

Step-by-step explanation:

Quadrilateral CDEF is inscribed in circle A, so:

m arc CDE + m arc CFE= 360°.

∠CFE and ∠CDE are inscribed angles, which means that their measures are one half the measure of their intercepted arcs.

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.

The correct option is C.