I tried to color code the degree measures in the diagram so that this was easier to follow. The black numbers are just what you’re given: ∠ABC measures 30° and ∠BDE measures 50°.
You’re also told that AB = BC, and that DE = EF = FD, which means the big triangle is isosceles, and the smaller, inner triangle is equilateral. The red numbers reflect the fact that ∠A and ∠C must be equal and add up to 150° since ∠B is 30°, and all the angles in an equilateral triangle are 60°.
From here, you can fill in more angles. To get ∠ADF, you recognize that AB is a straight segment, so its measure is 180°. You’ve already got a 50° and a 60° angle there, so ∠ADF must be 70° to make 180°. Then you have 2 of the 3 angles in triangle ADF, so you can solve for ∠DFA, which is 35°. The green numbers represent these last steps.
[For a bit more practice with triangles, read this post.]