(i) ∠DAC + ∠BAC = 180°(Linear pair)
120° + ∠BAC = 180°
∠BAC = 180° – 120°
= 60°
And,
∠ACD + ∠ACB = 180°
112° + ∠ACB = 180°
∠ACB = 68°
In ΔABC,
∠BAC + ∠ACB + ∠ABC = 180°
60° + 68° + x = 180°
128° + x = 180°
x = 180° – 128°
= 52°
(ii) ∠ABE + ∠ABC = 180°(Linear pair)
120° + ∠ABC = 180°
∠ABC = 60°
∠ACD + ∠ACB = 180°(Linear pair)
110° + ∠ACB = 180°
∠ACB = 70°
In ΔABC
∠A + ∠ACB + ∠ABC = 180°
x + 70° + 60° = 180°
x + 130° = 180°
x = 50°
(iii) AB ‖ CD and AD cuts them so,
∠BAE = ∠EDC (Alternate angles)
∠EDC = 52°
In ΔEDC
∠EDC + ∠ECD + ∠CEO = 180°
52° + 40° + x = 180°
92° + x = 180°
x = 180° – 92°
= 88°
(iv) Join AC
In ΔABC
∠A + ∠B + ∠C = 180°
(35° + ∠1) + 45° + (50° + ∠2) = 180°
130° + ∠1 + ∠2 = 180°
∠1 + ∠2 = 50°
In ΔDAC
∠1 + ∠2 + ∠D = 180°
50° + x = 180°
x = 180° – 50°
= 130°