Mathematics

An angle is such that the ratio between its complementary and supplementary angles is $1:4$. Then the angle measure is?

$60^o$

SOLUTION
Let the required angle be $x$

Then according to the question,
$\Rightarrow$  $\dfrac{90^o-x}{180^o-x}=\dfrac{1}{4}$

$\Rightarrow$  $4(90^o-x)=180^o-x$

$\Rightarrow$  $360^o-4x=180^o-x$

$\Rightarrow$  $360^o-180^o=-x+4x$

$\Rightarrow$  $180^o=3x$

$\Rightarrow$  $x=\dfrac{180^o}{3}$

$\therefore$  $x=60^o$
$\therefore$   The required angle is $60^o.$

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Single Correct Medium Published on 09th 09, 2020
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Subjects 10
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