(i)
∠BAD + ∠ABD + ∠ADB = 180 <em>the sum of the angles of a triangle equals 180°</em>
70 + 50 + ∠ADB = 180 <em>substituted given information</em>
∠ADB = 60 <em>subtraction property (subtracted 70 and 50)</em>
∠ABD + ∠BDC = ∠ADC <em>angle addition property</em>
60 + ∠BDC = 80 <em>substituted solved and given information</em>
∠BDC = 20 <em>subtraction property</em>
(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 <em>given as a hint</em>
∠BCA = 60 <em>substituted ∠ADB that was solved in part (i)</em>
Answer: (i) = 20, (ii) = 130?, (iii) = 60