Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary? (1 point)

Question

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 one half the measure of their intercepted arcs. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE. Using the _________________, 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.

inscribed angles; substitution property of equality

central angles; substitution property of equality

inscribed angles; addition property of equality

central angles; addition property of equality

Answer 1

The correct statements that complete the proof are:

inscribed angles; addition property of equality

So, the completed proof would read:

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 inscribed angles, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE = 2 ⋅ m∠CFE and m arc CFE = 2 ⋅ m∠CDE. Using the addition 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.