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