Question

The ratio of a pair of complementary angles is $2:3.$ Determine the angles.

• A. ${30}^o$
• B. ${36}^o$
• C. ${54}^o$
• D. ${60}^o$

Answer 1

Answer: (B), (C)

${54}^o$

The measure of a pair of complementary angles add up to ${90}^o.$
Let the pair of complementary angles be $x$ and $y.$

$\therefore x+y={90}^o$

Given: $\frac{x}{y}=\frac{2}{3}$
$\Rightarrow x=\frac{2y}{3}$
Substituting $x$ in the above equation we get,
$\frac{2y}{3}+y={90}^o$
$\Rightarrow \frac{2y}{3}+\frac{3y}{3}={90}^o$
$\Rightarrow \frac{2y+3y}{3}={90}^o$
$\Rightarrow \frac{5y}{3}={90}^o$
$\Rightarrow y=\frac{3\times {90}^o}{5}={54}^o$

$\therefore x={90}^o-y={90}^o-{54}^o={36}^o$

Hence, the pair of angles are ${36}^o$ and ${54}^o.$