Question

In the following 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°