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 _______________ Since arc DBE and arc DCE add up to the whole circle, or 360 degrees, the total of

Answer 1

∡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.

∡CBE is half of arc DCE
∡EDC is half of arc ECD
∡DCE is half of arc DBE
∡DBE is half of arc DCE