Question 175903
First - 
2 angles are complementary if their sum is 90 degrees
2 angles are supplementary if their sum is 180 degrees

Call the angle we are looking for x.  Then it's complement is 90-x and its supplement is 180-x.  (To see this think about an example - say x is 30 degrees.  Then its complement is 90-30=60 degrees and its supplement is 180-30=150 degrees.)

So, if the supplement of x is 10 degrees smaller than three times its complement, we can represent that by
{{{180-x=3(90-x)-10}}}
So, first, lets distribute through on the right hand side and group like terms.
{{{180-x=270-3x-10}}}
{{{180-x=260-3x}}}
Now, we need to solve for x.  First, we could add 3x to both sides.
{{{180+2x=260}}}
Now, subtract 180 from both sides.
{{{2x=80}}}
Lastly, dividing both sides by 2, we get that x=40.