Question

In the following figure, PQ, RS and UT are parallel lines. If c = 75° and `a = 2/5 c`, find b.

Answer 1

Since, PQ || UT and PT is transversal.

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

⇒ a + b = c

⇒ b = c – a  

⇒ `b = c - 2/5 c`  ...`[∵ a = 2/5 c, "given"]`

⇒ `b = (5c - 2c)/5`

⇒ `b = (3c)/5`

⇒ `b = (3 xx 75^circ)/5`  ...[∵ c = 75°, given]

⇒ b = 45°