Question

If two complementary angles are in the ratio 1:5, find the angles.

• A. ${35}^{\circ },{55}^{\circ }$
• B. ${16}^{\circ },{80}^{\circ }$
• C. ${30}^{\circ },{150}^{\circ }$
• D. ${75}^{\circ },{15}^{\circ }$

Answer 1

The correct option is D

${75}^{\circ },{15}^{\circ }$

Complementary angles are angles whose sum is ${90}^{\circ }$

Let the angles be $x^{\circ }and(90-x{)}^{\circ }$

$\Rightarrow \frac{x}{(90-x)}=\frac{1}{5}$

$\Rightarrow 5x=90-x$

$\Rightarrow 5x+x=90$

$\Rightarrow 6x=90$

$\Rightarrow x=\frac{90}{6}={15}^{\circ }$

$\Rightarrow (90-x)=(90-15)={75}^{\circ }$

$\therefore \text{The required angles are}{15}^{\circ }and{75}^{\circ }$