Question 81121
What you have here is 2 equations with 2 unknowns. Any time you have at least as many equations as unknowns, you can solve for the unknowns!
I will call the 2 angles in this problem A and B. Since you are given the fact that the angles are complementary, you know:
Equation #1: {{{A+B=90}}}
You also know from the given information that:
Equation #2: {{{A=3B+30}}}
So there are your 2 equations and 2 unknowns. You can use the substitution method to solve this. First, solve Equation #1 for B:
{{{A+B=90}}}
{{{B=90-A}}}
Now, substitute this expression for B into Equation #2:
{{{A=3B+30}}}
{{{A=3(90-A)+30}}}
{{{A=270-3A+30}}}
{{{4A=300}}}
{{{highlight(A=75)}}}degrees
Now that you have a value for angle A, substitute that back in to Equation #2 in order to find B:
{{{A=3B+30}}}
{{{75=3B+30}}}
{{{3B=45}}}
{{{highlight(B=15)}}}
And you are done.
Good Luck,
tutor_paul@yahoo.com