In the given figure the directed lines are parallel to each other.Find the unknown angles.
Answers
Answer:
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Step-by-step explanation:
(i) ∵ Lines are parallel
∴ a = b (Corresponding angles)
a = c (vertically opposite angles)
∴ a = b = c
But b = 60° (Vertically opposite angles)
∴ a = b = c = 60°
(ii) ∵ Lines are parallel
∴ x = z (Corresponding angles)
But z + y = 180° (linear pair)
But y = 55° (Vertically opposite angles)
∴ z + 55° = 180°
⇒ z = 180° - 55° ⇒ z = 125°
But x = z
∴ x = 125°
Hence x = 125°, y = 55°, z = 125°
(iii) ∵ Lines are parallel
∴ c = 120°
a + 120° = 180° (co – interior angles)
∴ a = 180° - 120° = 60°
But a = b (vertically opposite angles)
∴ b = 60°
Hence a = 60°, b = 60° and c = 120°
(vii) ∵ Lines are parallel
∴ x = p
And p + 120° = 180° (alternate angles)
⇒ p = 180° - 120° = 60°
∴ x = 60°
q = 120° (Corresponding angles)
y = 110° (Vertically opposite angles)
and ∠1 +110° = 180°
(co – interior angles)
∴ ∠1 = 180° - 110° = 70°
But z = ∠1 (vertically opposite angles)
∴ ∠z = 70°
Hence x = 60°, y = 110°, z = 70°,
p = 60°, q = 120°
(viii) ∴ Lines are parallel
∴ y = 75° (alternate angles)
∠1 +112° = 180° (linear pair)
∠1 = 180° - 112° = 68°
∠1 = x (Corresponding angles)
∴ x = 68°
But x + 75 + z = 180° (angles on a line)
⇒ 68° + 75° + z = 180°
⇒ z + 143° = 180°
⇒ z = 180° - 143° = 37°
Hence x = 68°, y = 75°, z = 37°
(ix) ∵ Line is parallel
∠a = ∠I and ∠c = ∠2 (alternate angles)
But ∠1 + 115° = 180° (linear pair)
∴ ∠1 = 180° - 115° = 65°
Similarly ∠2 + 120° = 180°
∴ ∠2 = 180° - 120° = 60°
∠ a = ∠1 = 65°,
∠c = ∠2 = 60°,
But a + b + c = 180° (angles on a line)
⇒ 65° + b + 60° = 180°
⇒ b + 125° = 180°
b = 180° - 125° = 55°
Hence a = 65°, b = 55°, c = 60°
(x) ∵ Lines are parallel
∴ x + 110° = 180° (co – interior angles)
x = 180° – 110° = 70°
and x + y = 180° (co – interior angles)
⇒ 70° + y = 180°
⇒ y = 180° – 70° = 110°
Z = y (Corresponding angles)
∴ z = 110°
Hence x = 70°, y = 110°, z = 110°
(xi) From 0, draw a line parallel to the given
Parallel lines
∵ Lines are parallel
∴ ∠1 = 160° and ∠2 = 130°
(Alternate angles)
∴ y = ∠1 + ∠2 = 160° + 130° = 290°
But x + y = 360° (angles at point)
⇒ 290° + x = 360°
⇒ x = 360° - 290° = 70°
Hence, x = 70°, y = 290°
(xii) From 0, draw a line parallel to the given parallel lines
∴ ∠1 = 50° (alternate angles)
∠2 = 40°
∴ b = ∠1 + ∠2 = 50° + 40° = 90°
But a + b = 360°
∴ a + 90° = 360°
⇒ a = 360° - 90° = 270°
Hence, a = 270°, b = 90°
