(i)
∠BAD + ∠ABD + ∠ADB = 180 the sum of the angles of a triangle equals 180°
70 + 50 + ∠ADB = 180 substituted given information
∠ADB = 60 subtraction property (subtracted 70 and 50)
∠ABD + ∠BDC = ∠ADC angle addition property
60 + ∠BDC = 80 substituted solved and given information
∠BDC = 20 subtraction property
(ii) SORRY but I'm not sure how to find ∠BCD. If ∠ADC = ∠ABC, then ∠DBC = 30. We already calculated ∠BDC = 20, which means that ∠BCD = 130
(iii)
∠BCA = ∠ADB given as a hint
∠BCA = 60 substituted ∠ADB that was solved in part (i)
Answer: (i) = 20, (ii) = 130?, (iii) = 60