Sum of Angles in Triangle Calculation

In triangle ABC, angle A measures 35 degrees and angle B measures 85 degrees. A line segment is drawn from point C to point D, where D lies on the side AB. If angle ACD measures x degrees and angle BCD measures y degrees, which is equal to the remaining angle in triangle CDB, calculate the value of x + y.

Use the following relationships:

• Sum of angles in a triangle equals 180 degrees.
• Angles A, B, and C in triangle ABC also sum to 180 degrees.