Question

PLEASE HELP! WILL MEDAL&FAN :)
Lines CD and DE are tangent to circle A as shown below:

Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 105 degrees. Point B lies on circle A.

If arc CE is 105°, what is the measure of ∠CDE?

52.5°
62.5°
75°
255°

Answer 1

do you need to show how to figure it out , or just use some formula thing they give you

Answer 2

i would like to know how to figure it out..

Answer 3

the formula for this problem is \[m<abc=1/2(major arc- minorarc)\]

Answer 4

you can show CAE and CDE are suppl anges

Answer 5

ive never used this formula before...

Answer 6

so to figure it out plug in the variables:

major arc = 255
minor arc = 105

Answer 7

m<CDE = 1/2(255-105)

Answer 8

Let's tackle this a little more theoric, let's say that we have an exterior angle "alpha" and we connect the two perpendicular bisectors to the origin, we obtain:

You see, we can calculate angle "alpha" by using the quadrilateral ABOC and obtaining the following relationship utilizing the very property that quadrilateral have two supplementary and opposite angles, meaning that alpha and beta must sum up to 180º:
\[\alpha + \beta = 180º\]
\[\alpha= 180º- \beta\]
And that is the formula to use.

Answer 9

oh wow thank you! :)

Answer 10

ur welcome!!!!

Answer 11

told you geometry is my thing!