Answer:

Two parallel lines l and m be cut a transversal t, forming angles.

It is given that ∠1:∠2=5:7

Let the measures of angles by 5x and 7x,

Then,

5x+7x=180

12x=180

x=180/12

x=15

∴∠1=5x=5×15=75

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∠2=7x=7×15=150

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We know that,

∠2+∠3=180

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......[∵ linear pair]

150

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+∠3=180

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=∠3=180−105

∠3=75

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∠3+∠6=180

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......[∵ the sum of the consecutive interioi angles is 180

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]

75

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+∠5=180

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∠6=180−75

∠6=150

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Now ∠6=∠8=150

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.....[∵ vertically opposite angles are equal]

∴∠1=75

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,∠2=105

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,∠=75

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and ∠8=105

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