a) From the figure, ∠A = 40°, ∠B = 60°, ∠D = 45°
Exterior angle at C = x°
Exterior angle at E = y°
Exterior angle of a triangle is equal to the sum of its opposite interior angles.
Exterior angle at C = ∠A + ∠B
x = 40° + 60°
∴ x = 100°
Exterior angle at E = ∠C + ∠D
y = x + 45°
y = 100° + 45°
∴ y = 145°
b) From the figure,
∠M = y, ∠N = 70°
Exterior angle at M = x°
Exterior angle at L = 120°
Exterior angle of a triangle is equal to the sum of its opposite interior angles.
Exterior angle at L = ∠M + ∠N = 120°
⇒ y + 70° = 120°
⇒ y + 70 – 70 = 120 – 70
∴ y = 50°
∠QLN + ∠MLN = 180° (linear pair of angles)
120° + ∠MLN = 180°
120° + ∠MLN – 120° = 180°- 120°
∠MLN = 60°
∴ ∠L = 60°
Exterior angle at M = ∠L + ∠N
x = 60° + 70° = 130°
∴ x = 130°
∴ x = 130° and y = 50°
