Question

The figure below shows Quadrilateral CDBE inscribed in a circle with center A.

The paragraph proof with missing statement proves that its opposite angles are supplementary. Which statement can be used to fill in the blank space?

Given that CDBE is a quadrilateral inscribed in a circle with center A, ∡DCE and ∡DBE are inscribed angles. Since the measure of an inscribed angle is one-half the measure of its intercepted arc, ∡DCE is half of arc DBE and ∡DBE is half of arc DCE. Since ____________________________ add up to the whole circle, or 360 degrees, the total of ∡DCE and ∡DBE must be half of 360, or 180 degrees. Therefore, they are supplementary. By the definition of a quadrilateral, all interior angles must add to 360. Therefore, the other two angles must also be supplementary.

arc DBE and arc DCE

arc BEC and arc BDC

∡BEC and ∡BDC

∡DCE and ∡DBE

Answer 1

It's "arc DBE and arc DCE" because they were just referenced in the last sentence. So it makes the most sense to logically follow with this statement.

Answer 2

Also, they're talking about arc measures because they're talking about two things that "add up to the whole circle"

Answer 3

thanks hun:)

Answer 4

sure thing