Question

f) If pair of complementary angles are in the ratio 4:11, find them only answer
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Answer 1

Given

• Pair of complementary angles are in the ratio 4:11.

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To find

• The angles.

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Solution

• Let the ratio of angles be x.

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Then,

$\tt\longrightarrow{First\: angle = 4x}$

$\tt\longrightarrow{Second\: angle = 11x}$

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We know that

$\sf\underline {Two \: angles \: are \: complementary \: if \: their} \\ \sf\underline {sum \: is \: 90°}$

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According to the question

$\tt:\implies\: \: \: \: \: \: \: \: {4x + 11x = 90}$

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$\tt:\implies\: \: \: \: \: \: \: \: {15x = 90}$

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$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{90}{15}}$

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$\bf:\implies\: \: \: \: \: \: \: \: {x = 6}$

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• By putting value of x

$\tt\longrightarrow{First\: angle = 4x = 24°}$

$\tt\longrightarrow{Second\: angle = 11x = 66°}$

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