Question
In the given figure, the directed lines are parallel to each other. Find the unknown angles.
✓
Answer
∵ 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°
∴ 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°
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