Question

Find the measure of an angle, if five times of its complement is ${24}^o$ less than twice of its supplement.

• A. $46$
• B. $38$
• C. $24$
• D. $32$

Answer 1

The correct option is B $38$

Two angles whose sum is ${180}^o$ are said to be supplementary.

Two angles whose sum is ${90}^o$ are said to be complementary.

Let the angle be $x$.

Given that $5(90-x)=2(180-x)-24$

$\Rightarrow 450-5x=360-2x-24\Rightarrow 5x-2x=450-360+24\Rightarrow 3x=474-360$

$\Rightarrow 3x=114\Rightarrow x=\frac{114}{3}$

$\Rightarrow x=38$

Therefore, the angle is ${38}^o$.