Question 500234
I'm not certain I understand the diagram,
It looks like you have a triangle ABC adjoining triangle ADC with the base on the bottom.
So, sides AC and BC are congruent, this is given,  and angle b is given as 38 degrees.
Since BC and AC are congruent, angle BAC is congruent to ABC at 38 degrees.
38 degrees and 38 degrees = 76 degrees, 180 - 76 degrees = 104 degress. for angle BCA.
This makes angle ACD 76 degreees, since they are adjoining angles on a linear angle.
Since AD and CD are congruent, angle ACD and CAD are congruent at 76 degrees.
So CAD = 76 degrees and BAC = 38 degrees, so angle BAD = 114 degees,
BAD + 114, plus ABC = 38 = 152 degress.
180 - 152 = 28 degrees For angle C.
Cleomenius.