Question

Iron rods a, b, c, d, e and f are making a design in a bridge as shown in figure, in which a || b, c || d, e || f. Find the marked angles between

1. b and c
2. d and e
3. d and f
4. c and f

Answer 1

Since, l, m are two parallel lines and PQ, RS and TU are transversal.

Then, ∠4 = ∠QPS  ......[Alternate interior angles]

⇒ ∠4 = 75°   ......[∵ ∠QPS = 75°]

Again, ∠1 = ∠QOR  ......[Vertically opposite angles]

⇒ ∠1 = ∠30°  ......[∵ ∠QPS = 30°]

Also, PQ and TU are parallel and m and l are traversal

Therefore, ∠2 + ∠QPT = 180°  ......[Consecutive interior angles]

⇒ ∠2 = 180 – 75°  ......[∵ ∠QPS = 75°, given]

⇒ ∠2 = 105°

Also, ∠2 + ∠3 = 180°

⇒ 105° + ∠3 = 180°

⇒ ∠3 = 180° – 105°

⇒ ∠3 = 75°

Hence, 

1. 30°
2. 105°
3. 75°
4. 75°