Question

A road crosses a railway line at an angle of 30° as shown in the following. Find the values of a, b and c.

Answer 1

Lines l and m are parallel, P is transversal and x = 30°

Therefore, 
 

⇒ y = 30°   ...[Corresponding angles]

Now, c + y = 180°  ...[Linear pair]

⇒ c + 30° = 180°

⇒ c = 180° – 30°

⇒ c = 150°

Now, ∠1 + c = 180°  ...[Linear pair]

⇒ ∠1 + 150° = 180°

⇒ ∠1 = 180° – 150° = 30°

∴ ∠1 = a  ...[Corresponding angles]

⇒ a = 30°

Also, ∠2 + a = 180°  ...[Linear pair]

⇒ ∠2 + 30° = 180°

⇒ ∠2 = 180° – 30° = 150°

Again, ∠2 = b  ...[Alternate interior angles]

⇒ b = 150°

Hence, a = 30°, b = 150° and c = 150°