Let x represent the measure of angle acd, and let y represent the measure of angle bcf. the value of x is ° and the value of y is

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°