The supplementary angle of an angle is $\frac{9}{4}$ times its complementary angle. Find the measure of the supplementary angle(in degree).

The correct option is C 162

$Letanglebex,thenitscomplementaryanglewillbe({90}^{\circ }-x)andsupplementaryanglewillbe({180}^{\circ }-x)$
$now({180}^{\circ }-x)=\left(\frac{9}{4}\right)({90}^{\circ }-x)4({180}^{\circ }-x)={810}^{\circ }-9x{720}^{\circ }-4x={810}^{\circ }-9x5x={90}^{\circ }\therefore x={18}^{\circ }$
$\therefore supplmentaryangle=180-18={162}^{\circ }$