Question

Two opposite anglrs ofa parallelligram are (5x-21) and (x+75). Find the measure of each angle of the parallelligram
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Answer 1

Given:-

• Opposite angles of parallelogram are (5x - 21) and (x + 75).

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To find:-

• Measure of each angle of parallelogram.

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SolutiOn:-

Let,

(5x - 21)° be ∠B

(x + 75)° be ∠D

And other two angles be ∠A and ∠C

So, Parallelogram will be ABCD.

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We know that,

Opposite angles of parallelogram are equal.

So,

➝ (5x - 21) = (x + 75)

➝ 5x - 21 = x + 75

➝ 5x - x = 75 + 21

➝ 4x = 96

➝ x = 96/4

➝ $\boxed{x = 24}$

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∠B = 5x - 21° = 5 × 24° - 21° = 99°

∠D = x + 75° = 24° + 75° = 99°

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We also know that,

Sum of two adjacent angles of parallelogram is 180°.

So,

➝ ∠A + ∠B = 180°

➝ ∠A + 99° = 180°

➝ ∠A = 180° - 99°

➝ ∠A = 81°

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As we know , Opposite angles of parallelogram are equal.

So,

➝ ∠A = ∠D = 81°

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Verification:-

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We know that,

Sum of all interior angles of parallelogram is 360°.

So,

➝ ∠A + ∠B + ∠C + ∠D = 360°

➝ 81° + 99° + 81° + 99° = 360°

➝360° = 360°

Hence, verified.

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According to parallelogram ABCD.

∠A = 81°

∠B = 99°

∠C = 81°

∠D = 99°

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Therefore,

First angle of parallelogram is 99°

Second angle of parallelogram is 81°.

Third angle of parallelogram is 99°.

Fourth angle of parallelogram is 81°.