Question

The supplement of an angle is one-third of itself. Determine the angle and its supplement.

Answer 1

Let the measure of the angle be $x^{\circ }$. Then, the measure of its supplementary angle is $(180-x{)}^{\circ }$.

According to given information,

$180-x=\frac{1}{3}x$

$3(180-x)=x$

$4x=540$

$x={135}^{\circ }$

Supplementary angle $={180}^{\circ }-{135}^{\circ }={45}^{\circ }$

Thus the measure of the angle is ${135}^{\circ }$ and the measure of its supplement is ${45}^{\circ }$.