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.
[tex]\begin{gathered} 180-x\text{ is the supplement} \\ 90-x\text{ is the complement} \end{gathered}[/tex][tex]\begin{gathered} 180-x=5(90-x) \\ 180-x=450-5x \\ 180-450=-5x+x \\ -270=-4x \\ divide\text{ both side by -4} \\ -\frac{270}{-4}=-\frac{4x}{-4} \\ x=67.5 \end{gathered}[/tex][tex]\begin{gathered} \text{supplement = 180 -x} \\ \text{supplement = 180 - 67.5} \\ \text{supplement = 112.5} \end{gathered}[/tex]
Hence the measure of the larger angle = 112.5
