(i) ∠DAC + ∠BAC = 180^o (Linear pair)

120^o + ∠BAC = 180^o

∠BAC = 180^o – 120^o

= 60^o

And,

∠ACD + ∠ACB = 180^o

112^o + ∠ACB = 180^o

∠ACB = 68^o

In ABC,

∠BAC + ∠ACB + ∠ABC = 180^o

60^o + 68^o + x = 180^o

128^o + x = 180^o

x = 180^o – 128^o

= 52^o

(ii) ∠ABE + ∠ABC = 180^o (Linear pair)

120^o + ∠ABC = 180^o

∠ABC = 60^o

∠ACD + ∠ACB = 180^o (Linear pair)

110^o + ∠ACB = 180^o

∠ACB = 70^o

In

∠A + ∠ACB + ∠ABC = 180^o

x + 70^o + 60^o = 180^o

x + 130^o = 180^o

x = 50^o

(iii) AB ‖ CD and AD cuts them so,

∠BAE = ∠EDC (Alternate angles)

∠EDC = 52^o

In

∠EDC + ∠ECD + ∠CEO = 180^o

52^o + 40^o + x = 180^o

92^o + x = 180^o

x = 180^o – 92^o

= 88^o

(iv) Join AC

In

∠A + ∠B + ∠C = 180^o

(35^o + ∠1) + 45^o + (50^o + ∠2) = 180^o

130^o + ∠1 + ∠2 = 180^o

∠1 + ∠2 = 50^o

In

∠1 + ∠2 + ∠D = 180^o

50^o + x = 180^o

x = 180^o – 50^o

= 130^o