Question

Two adjacent angles of a parallelogram are in the ratio of 4:5. Find all the angles of the parallelogram.


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Answer 1

Let ∠A and ∠B are two adjacent angles.

But we know that sum of adjacent angles of a parallelogram is 180

o

∠A+∠B=180

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Given that adjacent angles of a parallelogram are in the ratio 4:5 and let that ratio be multiple of x

∠A+∠B=180

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4x+5x=180

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9x=180

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x=180/9

x=20

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∠A=4x=4×20=80

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∠B=5x=5×20=100

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Also ∠B+∠C=180

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[Since ∠B and

∠C are adjacent angles]

100

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+∠C=180

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∠C=180

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−100

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=80

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Now, ∠C+∠D=180

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[Since ∠C and

∠D are adjacent angles]

80

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+∠D=180

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∠D=180

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−80

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=100

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Answer 2

$\huge\mathfrak\red{♡♡♡♡♡}$

$\huge\mathfrak\green{☟ \: \: \: \: answer \: \: \: \: \: ✎}$

$Let \: the \: Parallelogram \: is \: ABCD$

$The \: Adjacent \: \\ angles \: are \: 4x \: and \: 5x$

$Let \: ∠C = 4x, \: ∠B \: = \: 5x$

We know sum of adjacent angles is equal to

180°

$∠C+∠B=180°$

$4x+5x= 180$

$9x = 180$

$x = \frac{180}{9} = 20°$

$Then \: ∠C= 4x$

$= 4 \times 20 = 80°$

$∠B=5x$

$= 5 \times 20 = 100°$

Since opposite angles of Parallelogram are equal

$∠C=∠A=80°$

$∠B=∠D=100°$

$\\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$

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