If the supplement of an angle is  $\frac{5}{2}$times the complement of the same angle, find the supplementary angle.

Let the angle is a.

Its supplement = 180^o - a
Its complement = 90^o - a
${180}^{\mathrm{o}}-\mathrm{a}=\frac{5}{2}\times ({90}^{\mathrm{o}}-\mathrm{a})$
$\Rightarrow {180}^{\mathrm{o}}-\mathrm{a}=\frac{({450}^{\mathrm{o}}-5\mathrm{a})}{2}$
$\Rightarrow {360}^{\mathrm{o}}-2\mathrm{a} = {450}^{\mathrm{o}} - 5\mathrm{a}$
$\Rightarrow 3\mathrm{a}={90}^{\mathrm{o}}$
$\Rightarrow \mathrm{a}={30}^{\mathrm{o}}$
So, the angle is 30^o, and its supplement $=150°$