Supplement of an angle is one fourth of itself. The measure of the angle is :

The correct option is C ${144}^o$

Let one angle be $x^o$. Then, another angle is ${\frac{x}{4}}^o$.

Thus, $x+\frac{x}{4}={180}^o$

$5x=180\times 4$

$x=\frac{180\times 4}{5}={144}^o$

Thus, the required angles are ${144}^o,{36}^o$.