Question

In the adjoining figure, l ∥ m and ∠1 and ∠2 are in ratio 4 : 5.

find the value of all angles from 1 to 8​

Answer 1

$\underline{\underline{\sf{\green{Appropriate \: Question :\::-}}}}$

• In the adjoining figure, l ∥ m and ∠1 and ∠2 are in ratio 4 : 5. find the value of all angles from 1 to 8

$\underline{\underline{\sf{\blue{Given\::-}}}}$

• ∠1 : ∠2 = 4 : 5

$\underline{\underline{\sf{\blue{To\:Find\::-}}}}$

• The value of all angles from 1 to 8

$\underline{\underline{\sf{\green{Required \: Solution\::-}}}}$

Let common factor be x.

↦ ∠1 : ∠2 = 4x : 5x

Now,

∠1 + ∠2 = 180° (Linear pair)

↪ 4x° + 5x° = 180°

↪ 9x° = 180°

↪ x = 180°/9 = 20°

Hence,

∠1 = 4x° = 4 × 20° = 80°

∠2 = 5x° = 5 × 20° = 100°

∠1 = ∠5 = 80°( corresponding angles)

∠1 = ∠3 and ∠5 = ∠7 (vertically opposite angles)

∴ ∠1 = ∠3 = ∠5 = ∠7 = 80°

∠2 = ∠6 = 100° (corresponding angles )

∠2 = ∠4 and ∠6 = ∠8 (vertically opposite angles)

∠2 = ∠4 = ∠6 = ∠8 = 100°

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