Hello from MrBillDoesMath!
Answer: x - 90, y = 43
Discussion:
The triangles are congruent by the SAS theorem. (In left triangle, side = AB, angle = y; other side = AD). Because of congruence, angle ADC = x and (x + x = 180) as BDC is a straight line. So 2x = 180,or x = 90.
In the leftmost triangle : y + angle B + angle x = 180 as the sum of all angles in a plane triangle is 180 degrees. But angle B = angle C = 47 degrees as triangle ABC is isosceles. Putting this all together:
y + angle B + angle x = 180 =>
y + 47 + x = 180 =>
y + 47 + 90 = 180 =>
y + 137 = 180 =>
y = 180 - 137 = 43
Thank you,
MrB
