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# The supplementary angle of an angle is$\dfrac{9}{4}$times its complementary angle. Find the measure of the supplementary angle (in degree).$(a)144$$(b)126$$(c)162$$(d)108$

Last updated date: 15th Jul 2024
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Hint: Take a variable angle and write down its supplementary and complementary angle , now make equations using given information to proceed.

Let the angle be$x$, then its complementary angle will be$\left( {{{90}^0} - x} \right)$
and supplementary angle will be$\left( {{{180}^0} - x} \right)$
now, it is given in the question that the supplementary angle of an angle is$\dfrac{9}{4}$times its complementary angle, that is
$({180^0} - x) = \left( {\dfrac{9}{4}} \right)({90^0} - x)$
$4 \times ({180^0} - x) = 9 \times ({90^0} - x)$
$4 \times ({180^0} - x) = {810^0} - 9x$
${720^0} - 4x = {810^0} - 9x$
$- 4x + 9x = {810^0} - {720^0}$
$5x = {90^0}$
$x = \dfrac{{{{90}^0}}}{5}$
$\therefore x = {18^0}$
Therefore, the supplementary angle$= {180^0} - {18^0} = {162^0}$
Hence, the required solution is$(c)162$.

Note: Assume the angles of the triangle according to the conditions given in the solution and then further evaluate to obtain the required solution.