Question 1045759
The trick to this is knowing that complementary angles add to be 90 degrees and supplementary angles add to be 180 degrees.
Let the angle be: X
It's complement is 4 times as large so it is: 4X
In words: angle + complement = 90
The equation to solve then is:
{{{X+4X=90}}}
{{{5X=90}}}
{{{5X/5=90/5}}}
{{{X=18}}} 
That is the measure of the angle {{{highlight(18)}}}
It's complement is 4X so 4(18) is {{{highlight(72)}}}
For the supplement in words:
angle +  its supplement = 180
We already used X, so let's let the supplement be: Y
{{{18+Y=180}}}
{{{18+Y-18=180-18}}}
{{{Y=162}}}
So the supplement is {{{highlight(162)}}}
If you are in algebra 2, they may have wanted you to use two equations, two unknowns...but you should get the same result.
Happy Calculating!