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

$(a)144$

$(b)126$

$(c)162$

$(d)108$

Answer

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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.

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.

Last updated date: 25th Sep 2023

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