Geometry help.?

Question

Line AD bisects angle BAC. Line CD bisects angle ACE. AB is parallel to CE. Find angle ADC and show work. Figure:

____________A______________________B
....................._
..................._....................D
_________C________________________E
Pretend AC, AD, and CD are connected.

Answer 1

AB is parallel to CE and AC is a transverse... that is AC cut both.

Then angles BAC and ACE are inner and in the same side of the transverse... a theorem say BAC + ACE = 180 degrees

Suppose BAC = 2x and ACD = 2y ... and then 2x + 2y = 180 or x+y = 90

The angles inside the triangle ACD are x, y and ADC and thus,
ACD + x + y = 180 (degree)

ACD + 90 = 180 then ACD = 90 (degree)

Answer 2

Angle ADC is 90 degrees.

I am assuming that by bisecting you mean dividing the angles equally into two parts.
Then assume that AD bisects BAC into x and x.
Assume CD bisects ACE into y and y.
Now AB is parallel to CE.
Sum of Interior angles equal 180 degrees.
So x + x + y + y = 180.
so, 2x + 2y = 180
or x + y = 90.

Now, ADC make a triangle so the sum of the angles in the triangle is 180 degrees.
Assume angle ADC is z.
Then, x + y + z = 180.

We alrealy know from above that x + y = 90.
Therefore, z = 180 - (x+y) = 180 - 90.
So the answer is 90 degrees.

Answer 3

b.............e
l......d......l
l...../..\.....l
^.../.....\...^
l../........\..l
a/--------\c
Dots are only for spacing, and the answer is 90 degrees