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?

Answer 1

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, ______________________ and ∡DBE is half of arc DCE. Since arc DBE and arc DCE 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. (5 points)
∡CBE is half of arc DCE
∡EDC is half of arc ECD
∡DCE is half of arc DBE
∡DBE is half of arc DCE

Answer 2

ang DCE=1/2 of arc DBE, Is it correct?

Answer 3

I'm not sure....
I'm really confused.

Answer 4

@experimentX Sorry I keep bothering you, but could you please look at this as well? I'm really confused.

Answer 5

Angle subscribed by any arc at perimeter is HALF of the angle subscribed by the same ac at the center.

Answer 6

No worry. I am a math tutor. Botheration is my hobby.Ha ha ha

Answer 7

∡DCE is half of arc DBE

Answer 8

Oh, okay! Thanks so much!

Answer 9

ur welcome