Question

The measure of an angle is four times the measure of its supplementary angle. Then the angles are __________.

• A. ${36}^o,{144}^o$
• B. ${40}^o,{160}^o$
• C. ${18}^o,{72}^o$
• D. ${50}^o,{200}^o$

Answer 1

Answer: (A)

${36}^o,{144}^o$

According to the problem,

The measure of an angle which is $4$ times its supplement.

Supplementary angles means, sum of angles is ${180}^o$

Let the measure of one angle be $x$, then the measure of its supplementary angle will be $({180}^o-x)$.

According to the given condition,

$⟹x=4({180}^o-x)$

$⟹x=4\times {180}^o-4x$

$⟹5x=4\times {180}^o$

$⟹x=4\times {36}^o={144}^o$

Hence, $x={144}^o$

so these angles are ${36}^{\circ }$, ${144}^{\circ }$

Hence the option $\left(A\right)$ is correct.