Answer:
x= 34°
y=5
Because segments AB and BC are congruent, their corresponding angles (<BAD and <BCD) would also be congruent to each other, meaning that both would be 56°.
Knowing that triangles add up to 180°, the whole triangle (ABC) would then have 2 angles that are 56° and the top angle (<ABC) would be 68°
Splitting those in half ( because <ABD and <CBD are congruent), each would be 34° (thus x=34°)
Looking now at the two separate triangles (ABD and CBD), we can determine that both <BDA and <BDC are 90° (right angles) because 180-34-56=90°.
Therefore, since both triangles have all congruent angles, both triangles are the same! So, since segment AD=5, segment CD would also be 5 (y=5).
