Courses
Courses for Kids
Free study material
Free LIVE classes
More

# 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: 26th Mar 2023
Total views: 309k
Views today: 8.85k
Verified
309k+ views
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.