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

please help

Answer 2

@whpalmer4 can you please help me with this question its getting me frustrated.

Answer 3

@jim_thompson5910 can you help me with this qeustion please?

Answer 4

@mathstudent55 can you help me with this question?

Answer 5

@amistre64 can you help me wuth this question afterwards if your fine with that.

Answer 6

∡CBE is half of arc DCE

∡DBE is half of arc DCE

∡DCE is half of arc DBE

∡EDC is half of arc ECD

Answer 7

@phi and @campbell_st can you guys help me???

Answer 8

well, its the other part of the arc setup ....

Answer 9

angle dbe to arc dce

Answer 10

do you know how to do this phi??

Answer 11

probably

Answer 12

you have to take it line by line, and make sense of each line.
first
∡DCE and ∡DBE are inscribed angles.

can you find those angles in the picture ?
do you know what " inscribed angle" means?

Answer 13

formed when two secant lines of a circle intersect a circle

Answer 14

∡DCE is half of arc DBE

what does that mean ?

Answer 15

that mean that it ishalf of arc DBE

Answer 16

yes,

now notice that arc DBE plus arc DCE is the whole circle, 360º
make sense ?

Answer 17

yeah i believe on thinking like that would help.

Answer 18

now what angle is 1/2 of arc DCE ?

Answer 19

so the possible answer can be arc DBE is half of arc DCE??

Answer 20

not arc DBE, *inscribed angle* DBE

Answer 21

i mean angle DBE

Answer 22

yeah.... sorry

Answer 23

so the answer will be inscribed angle DBE is half of arc DCE?? because that is what i am believing the answer will be that because of you hints it makes the most sense.

Answer 24

so we have these facts

∡DCE = 1/2 arc DBE
∡DBE = 1/2 arc DCE

add together:

∡DCE + ∡DBE = 1/2 arc DBE + 1/2 arc DCE

factor out the 1/2
∡DCE + ∡DBE = 1/2 ( DBE + DCE)
but we know DBE +DCE (arcs) = 360 degrees

Answer 25

and we get
∡DCE + ∡DBE = 1/2 (360)
∡DCE + ∡DBE = 180 degrees

that is the proof they are going through.

they want you to fill in the the part ∡DBE = 1/2 arc DCE

Answer 26

ok thanks for your help!!!

Answer 27

and if you remember this result, it might come in handy to prove things... if you can remember that a quadrilateral inscribed in a circle has opposite angles that add up to 180

Answer 28

ok