Angle question?

Question

Line AC is congruent to Line BC. Ab is congruent with line AD. Line AD is conguent to DC. Find angle C and show work
Figure: A_C
...........B (D is between b and c, but also connects with a.)

Answer 1

I think you have a triangle ABC with point D on side BC so that AB = AD = DC. Also, AC = BC.

Let c be the measure of angle C.
In triangle ADC, since AD = DC, then angle DAC = angle DCA = angle C = c. So angle ADC = 180 - 2c.

Since B, D, and C are on the same line, angle ADB = 180 - angle ADC = 2c. In triangle ABD, AB = AD, so angle ABD = angle ADB = 2c. Then angle BAD = 180 - 4c.

In triangle ABC, AC = BC, so 2c = angle ABD = angle ABC = angle BAC = angle BAD + angle DAC = 180 - 4c + c.

Then 2c = 180 - 3c, or 5c = 180. Thus c = 36.