Question

Complement of half of an angle is ${24}^{\circ }$ more than one-third of its supplement. Find the angle.

• A. ${36}^{\circ }$
• B. ${44}^{\circ }$
• C. ${68}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is A ${36}^{\circ }$

Let $x$ be the angle.

Complement of half of the angle = $90-\frac{x}{2}$

Supplement of the angle =$180-x$

From the condition we have,

$90-\frac{x}{2}=\frac{1}{3}(180-x)+24$

$90-\frac{x}{2}=\frac{1}{3}\times 180-\frac{x}{3}+24$

$90-\frac{x}{2}=60-\frac{x}{3}+24$

$90-\frac{x}{2}=84-\frac{x}{3}$

$90-84=\frac{x}{2}-\frac{x}{3}$

$\frac{3x-2x}{6}=6$

$\frac{x}{6}=6$

$x=6\times 6$

$x={36}^{\circ }$