Question

In the given figure, the directed lines are parallel to each other. Find the unknown angles.

Answer 1

∵ Lines are parallel

∴ x + 90° = 180° ...........(co-interior angles)

⇒ x = 180°− 90° = 90°

⇒ ∠2 = x

⇒ ∠2 = 90°

But ∠1 + ∠2 + 30° = 180° ..........(sum of angles of a triangle)

⇒ ∠1 + 90° + 30° = 180°

⇒ ∠1 + 120° = 180°

⇒ ∠1 = 180°− 120° = 60°

But ∠1 = k ..........(vertically oposite angle)

∴ k = 60°

But ∠1 = z ......(alternate angles)

∴ z = 60°

But k + y = 180° .........(co-interior angles)

⇒ 60° + y = 180°

⇒ y = 180°− 60° = 120°

Hence x = 90°, y = 120°, 
z = 60°, k = 60°