Question

If an angle is ${28}^o$ less than its complement, find its measure.

• A. ${31}^o$
• B. ${131}^o$
• C. ${28}^o$
• D. ${32}^o$

Answer 1

The correct option is A ${31}^o$

Let the required angle be $x$.

Then, its complement $=({90}^o-x)$.

Given, the angle is ${28}^o$ less than its complement.

Then, $x=({90}^o-x)-{28}^o$

$\Rightarrow x+x={90}^o-{28}^o$

$\Rightarrow 2x={62}^o\Rightarrow x={\frac{62}{2}}^o\Rightarrow x={31}^o$.

Therefore, option $A$ is correct.