Question

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.
∡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

@experimentX & @FoolForMath

Answer 3

@Blahh23 it's easy for users if you post a pic. All don't have Microsoft word.
Here is the figure for your question

Answer 4

okay thanks:)

Answer 5

@satellite73 can you try and help me with this please..

Answer 6

Given angle DBE is half of arc DCE
Since DCE is also an inscribed angle, it's also half of some arc. Which is the arc?
Just read the question again, you'll be able to tell the answer

Answer 7

of DBE??

Answer 8

How did you find this?

Answer 9

DCE is half of arc DBE i think is what you want, hard to keep track with all these letters

Answer 10

@ash2326 is this right?

Answer 11

Yeah @satellite73

Answer 12

okay! thats what i thought! :) Thanks:)