Question

The supplement of an angle is 12 more than twice its complement. Find the complement of the supplement of the angle.

Answer 1

complimentary angles add up to 90 degree

supplimentary angle add up to 180 degree

Let the angles be x and y

Therefore,

$\begin{gathered} x+y=90^{\circ},x=90^{\circ}-y \\ x+y=180,x=180-y \\ the\text{ supplement }of\text{ an angle is 12 more than twice its compliment} \\ Thereofore, \\ 180-y=2(90-y)+12 \\ 180-y=180-2y+12 \\ -y+2y=12 \\ y=12 \end{gathered}$

Let us find the suppliment and compliment of the angle y.

$\begin{gathered} x=90-12=78^{\circ}\text{ ( compliment of the angle y)} \\ x=180-12=168^{\circ}\text{ (suppliment of the angle y)} \end{gathered}$