Question

Let x represent the measure of angle ACD, and let y represent the measure of angle BCF.

Answer 1

We know that
in the triangle ACB
∠ACB+90+34=180-----> ∠ACB=180-(90+34)----> ∠ACB=56°
∠ACD and ∠ACB-----> are supplementary angles
so
∠ACD+∠ACB=180-----> ∠ACD=180-56----> 124°------> x=124°

the answer Part 1) is x=124°

Part 2)
∠ACB+∠BCF+80=180-----> ∠BCF=180-(∠ACB+80)---> 180-(56+80)
∠BCF=180-136----> 44°-----> y=44°

the answer Part 2) is y=44°