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