(i) x + 50° = 120°
[By the exterior angle property of a triangle]
x= 120° – 50° = 70°
By Angle sum property of a triangle
x + y + 50° = 180°
x + y = 180° – 50° = 130°
70° + y = 130°
y = 130° – 70° = 60°
∴ x = 70°, y = 60°
(ii) 50° + y° + x° = 180°
∠y = 80° [vertically opposite angles]
50° + 80° + x° = 180°
(Angle sum property of a triangle)
130° + x = 180°
x° = 180° – 130° = 50°
[∴ x = 50°, y = 80°]
(iii) ∠x = 50° + 60° = 110°
[By exterior – angle property of a triangle]
y + 50° + 60° = 180°
( By Angle sum property of a triangle)
y + 110° = 180°
∴ y = 180° – 110° = 70°
∴ y = 70°, x = 110°
(iv) ∠x = 60°
[vertically opposite angles]
30° + x° + y° = 180°
(By Angle sum property of a triangle)
30° + 60° + y° = 180°
90° + y° = 180°
∴ y°= 180° – 90° = 90°
∴ x = 60° y = 90°
(v) ∠y = 90°
[vertically opposite angles]
∠x + ∠x + ∠y = 180°
(Angle sum property of a triangle)
2x + y° = 180°
2x + 90° = 180°
2x = 180° – 90°= 90°
x \(\frac{90^o}{2}\) = 45°
∴ ∠x = 45° & ∠y = 90°
(vi) ∠x ∠y
[vertically opposite angles]
∠x + ∠x + ∠y = 180°
(Angle sum property of a triangle)
2x + ∠y = 180°
2x + x° = 180° (∵ y = x)
3x = 180°
x = \(\frac{180^o}{3}\) = 60°
∴ x = 60° & y = 60°
