Question

The measure of two abjacent angles of a parallelegram are in the ratio 4:5. Find the measure of each of the parallelogram.


Be quick pls ​

Answer 1

⋆ Refrence of image is shown in diagram:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\sf P}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\sf Q}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\sf S}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\sf R}\qbezier(5.4,1)(5.2,1.4)(6.1,1.5)\qbezier(1.5,1)(1.6,1.5)(1.1,1.5)\put(1.5,1.5){\sf 4x}\put(5.2,1.5){\sf 5x}\end{picture}$

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GivEn that,

• The measure of two adjacent angles of a parallelegram are in the ratio 4:5.

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Therefore,

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☯ Let two adjacent angles 4x and 5x.

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Where,

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• ∠P = 4x
• ∠Q = 5x

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We know that,

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• Sum of adjacent angles of a parallelogram is 180°.

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Therefore,

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➯ ∠P + ∠Q = 180°

➯ 4x + 5x = 180°

➯ 9x = 180°

➯ x = 180/9

➯ x = 20°

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Hence,

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• ∠P = 4x = 4 × 20 = 80°

• ∠Q = 5x = 5 × 20 = 100°

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Also,

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∠Q and ∠R are adjacent angles,

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➯ ∠Q + ∠R = 180°

➯ 100° + ∠R = 180°

➯ ∠R = 180° - 100°

➯ ∠R = 80°

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Now,

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∠R and ∠S are adjacent angles. So,

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➯ ∠R + ∠S = 180°

➯ 80° + ∠S = 180°

➯ ∠S = 180° - 80°

➯ ∠S = 100°

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∴ Hence, all angles of parallelogram ∠P, ∠Q, ∠R and ∠S are 80°, 100°, 80° and 100° respectively.

Answer 2

Answer:

$\huge \bf \: Given$

$\sf \: measure \: of \: adjacent \: sides \: = 4 \ratio5$

$\huge \bf \: To \: find$

$\sf \: measure \: of \: each \: sides$

$\huge \bf \: Solution$

Let us assume sides be 4x and 5x.

As we know that sum of all sides of a parallelogram= 180⁰

Therefore,

$☯ \bf \: 4x + 5x = 180$

Now finding x

$\sf \implies \: 4x + 5x = 180$

$\sf \implies \: 9x = 180$

$\sf \implies \: x \: = \dfrac{180}{9}$

$\sf \implies \: x \: = 20$

$\huge \mathfrak {☯ \: x \: = 20 \degree}$

Hence,

$\sf \: 4x = 4(20) = 80$

$\sf \: 5x = 5(20) = 100$

Hence, all angles of parallelogram are 80°, 100°, 80° and 100° respectively.