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Question
In the given figure, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?
Options
∠1 = ∠3
∠2 = ∠4
∠6 = ∠7
∠4 = ∠8
Solution
∠4 = ∠8
Explanation:
From the given figure, PQ || RS and l is transversal, Therefore,
∠1 = ∠3 ...[Corresponfing angles]
∠2 = ∠4 [Corresponding angles] ...(i)
Also, ∠5 = ∠6 [Vertivally opposite angles] ...(ii)
And ∠5 = ∠7 [Corresponding angles] ...(iii)
⇒ ∠6 = ∠7 ...[From equations (ii) and (iii)]
Also, ∠2 + ∠8 = 180° ...[Linear pair]
⇒ ∠4 + ∠8 = 180° ...[∠2 = ∠4]
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