Answer:
∠ DCF = 45°
Explanation:
given AB is parallel to CD , then
∠ BAF and ∠ AEC are alternate angles and are congruent , that is
∠ AEC = ∠ BAF = 75°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ AEC is an exterior angle of Δ CEF , then
∠ DCF + ∠ CFA = ∠ AEC
∠ DCF + 30° = 75° ( subtract 30° from both sides )
∠ DCF = 45°