Question

The complement of an angle is one fourth of the measure of the angle. Find the measure of the angle.

• A. ${80}^{\circ }$
• B. ${72}^{\circ }$
• C. ${62}^{\circ }$
• D. ${58}^{\circ }$

Answer 1

The correct option is B

${72}^{\circ }$

Let the angle be $x^{\circ }$.

Then the complementary angle = $\frac{x^{\circ }}{4}$

$x+\frac{x}{4}={90}^{\circ }$ [ Since the angles are complementary]

$\Rightarrow \frac{4x+x}{4}={90}^{\circ }$

$\Rightarrow \frac{5x}{4}={90}^{\circ }$

$\Rightarrow x=\frac{{90}^{\circ }\times 4}{5}$

$\Rightarrow x={72}^{\circ }$

Required angle = ${72}^{\circ }$