Question

The angles of a quadrilateral are in the ratio 2:3:5:8. Find the measures of
all the angles.

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Ratio of angles = 2 : 3 : 5 : 8

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Measure of each angle = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Sum\: of\: all\:angles\:of \: quadrilateral = \: 360}}}}$

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• Let the angles be 2x , 3x , 5x , 8x

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$\sf: \implies\: {\bold{ 2x + 3x + 5x + 8x = 360}}$

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$\sf: \implies\: {\bold{ 18x = 360}}$

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$\sf: \implies\: {\bold{ x = \dfrac{360}{18}}}$

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$\sf: \implies\: {\bold{ x = 20 }}$

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• Putting value of x in each angles

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2x = 2 × 20 = 40

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3x = 3 × 20 = 60

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5x = 5 × 20 = 100

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8x = 8 × 20 = 160

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Angles of a quadrilateral are 40 , 60 , 100 , 160