Question

the measure of the supplement of an angle is five times that of the angle's complement. find the measure of the larger angle

Answer 1

To determne the measure of the larger angle:

Supplementary angles add up to 180 degrees.

Complementary angles add up to 90 degrees.

X is the angle.

`\begin{gathered} 180-x\text{ is the supplement} \\ 90-x\text{ is the complement} \end{gathered}`

`\begin{gathered} 180-x=5(90-x) \\ 180-x=450-5x \\ 180-450=-5x+x \\ -270=-4x \\ divide\text{ both side by -4} \\ -(270)/(-4)=-(4x)/(-4) \\ x=67.5 \end{gathered}`

`\begin{gathered} \text{supplement = 180 -x} \\ \text{supplement = 180 - 67.5} \\ \text{supplement = 112.5} \end{gathered}`

Hence the measure of the larger angle = 112.5