Question 99453
Ok first thing is to define supplementry angles. Which is: Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees.
So lets set angle one equal to x
and angle two equal to y
Now we can say 
{{{x+y=180}}}
Ok now as you problem states we want to find the measure of an angle
whose supplement is five times its measure.
Like you stated the angle we want to find is x. Angle x's supplement is y.
So if the supplement (angle y) is equal to five times angle x then
{{{y=5x}}}
Now since we know {{{x+y=180}}} and we know {{{y=5x}}} we can
replace the y in {{{x+y=180}}} with 5x like so
{{{x+5x=180}}} 
now we can solve for x
{{{x+5x=180}}}
{{{6x=180}}}
{{{x=30}}}
so if x=30 then y=150 
The angles are supplementry because they add up to 180
and angle y is 5 times angle x