Question

the measures of adjacent angles of parallelogram are in the ratio 5:4 find the measure of each angles of parallelogram ​

Answer 1

Step-by-step explanation:

Let ∠A and ∠B are two adjacent angles.

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

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∠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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