If ADC = 114, then BDC = 180-114 = 66.
Since BC is congruent to DC, angle BDC is congruent to angle DBC, which is also 66 degrees
The angle measures of triangle BCD must add up to 180 degrees, so 66+66 = 132 and 180 - 132 = 48. So angle BCD = 48.
Now, side AB is congruent to side AC, so angle ABC is equal to angle ACB.
Can you solve it from there? (hint - angle ABC is also angle DBC.)
You are very welcome!
:P