Question

Find the angles in each of the following.
The angle which is four times its supplement

• A. ${144}^{\circ }$
• B. ${44}^{\circ }$
• C. ${14}^{\circ }$
• D. None of these

Answer 1

The correct option is A ${144}^{\circ }$

Two Angles are Supplementary when they add up to 180 degrees.

Let the $\angle B$ is supplement of $\angle A$

Now according to question $\angle A=x$ then $\angle B=4x$

Hence $\angle B+\angle A=x+4x={180}^o$

$⟹5x={180}^o⟹x={36}^o$

$\angle A={36}^o$ and $\angle B=(4\times {36}^o)={144}^o$

Since $\angle B$ is $4$ times its supplement $\angle A$.

So the angle which is four times its supplement ${144}^o$.