Question

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

Answer 1

∵ 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°

Answer 2

We are given:

• One angle on the straight line is 75^∘

• Angles on a straight line form a linear pair, so:
  z = 180^∘ − 75^∘ = 105^∘

Sum of angles in triangle = 180^∘

112^∘ + y + 105^∘ = 180^∘

y = 180^∘ − (112^∘ + 105^∘) = 180^∘ − 217^∘ = −37

Angle = 180^∘ − 112^∘ = 68^∘

Now use triangle angle sum:

y + z + 68^∘ = 180^∘

y + 105^∘ + 68^∘ = 180^∘

y = 180^∘ − 173^∘ = 7^∘

x = 7^∘

y = 7^∘

z = 105^∘