(i) Interior angles ∠C + 120° = 180°
∠C = 180° – 120° = 60°
∵ ∆ABC is an isosceles triangle where
AB = AC
⇒ ∠B =∠C = 60° = y
∵ ∠A + ∠B +∠C = 180°
x + 60° + 60° = 180°
x = 180° – 120° = 60°
∴ x = 60° and y = 60°
(ii) ∠ABC is an isosceles triangle where BC =AC
BC = AC
⇒ ∠A = ∠B = x
and ∠A + ∠B = 90° [∵ ∠C = 90°]
⇒ x + x = 90°
⇒ 2x = 90°
⇒ x = 90/2 = 45°
But ∠B +1 = 180°
x + y = 180°
⇒ 45° + y = 180°
⇒ y = 180° – 45 = 135°
∴ x = 45° and y = 135°
(iii) ∆ABC is an isosceles triangle where AB = AC
AB = AC
⇒ ∠B = ∠C
or ∠B =∠C = x
and ∠A = 92° [vertically opposite angles]
∠A + ∠B + ∠C = 180°
92° + x + x = 180°
⇒ 2x = 180° – 92° = 88°
⇒ x = (88/2) = 44°
and ∠C + y = 180° [Linear pair]
⇒ y = 180° – 44° [∵∠C = x = 41°]
= 136°
∴ x = 44° and y = 136°
