Question

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

Answer 1

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, __________________________________
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.

∡DCE is half of arc DBE

∡EDC is half of arc ECD

∡CBE is half of arc DCE

∡DBE is half of arc DCE

Answer 2

use this:
"Since the measure of an inscribed angle is one-half the measure of its intercepted arc"

which option accurately shows an inscribed angle equaling half its arc?

Answer 3

the last one?

Answer 4

yes but they already use that one, what is the other one?

Answer 5

EDC is half of arc ECD???

Answer 6

EDC is not a valid angle of the quadrilateral....they give you the answer later on in the paragraph

Answer 7

oh woow that makes me feel dumb -.- so its the first one?

Answer 8

yep

Answer 9

thanks soo so much i would ask you to help me with others but i dont wanna bother you further so maybe il ask you something else in the future!

Answer 10

ok , glad to help