Question

In the given figure, PQ, RS and UT are parallel lines. If c = 57° and a = `c/3`, find the value of d.

Answer 1

Since, PQ || UT and PT is transversal,

Therefore, ∠QPT = ∠UTP  ......[Alternate interior angles]

⇒ a + b = c

⇒ `c/3` + b = c  ......`[∵ a = c/3, "given"]`

⇒ b = `c - c/3`

⇒ b = `(3c - c)/3`

⇒ b = `(2c)/3 = 2/3 xx 57^circ`  ......[∵ c = 57°, given]

∴ b = 38°

Again, PQ || RS and PR is transversal

Therefore, ∠QPR + ∠PRS = 180°  ......[Consecutive interior angles]

⇒ b + d = 180°

⇒ d = 180° – b

⇒ d = 180° – 38°  ......[∵ b = 38°]

⇒ d = 142°