Question

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

• A. ${45}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${60}^o$

Let the required angle be $x$

Then according to the question,

$\Rightarrow$ $\frac{{90}^o-x}{{180}^o-x}=\frac{1}{4}$

$\Rightarrow$ $4({90}^o-x)={180}^o-x$

$\Rightarrow$ ${360}^o-4x={180}^o-x$

$\Rightarrow$ ${360}^o-{180}^o=-x+4x$

$\Rightarrow$ ${180}^o=3x$

$\Rightarrow$ $x=\frac{{180}^o}{3}$

$\therefore$ $x={60}^o$

$\therefore$ The required angle is ${60}^o.$