SOLUTION: 9. In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle. [The sum of the measures of th

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Let a, b and c be the 3 angles. Since there are 3 variables, we're gonna need (at least) 3 equations to solve for them. Being a triangle we know:
Equation 1:


"one angle is double the measure of a second angle":
Equation 2:


"but is 10 degrees less than the measure of the third angle":
Equation 3:


Let's re-write equations 2 & 3 in terms of "a" so we can substitute them into equation 1.
Equation 2 can be rewritten as:

Equation 3 can be rewritten as:



Substituting back into Equation 1 gives us:

I prefer not to work with fractions if I can help it, so let's multiply every element, on both sides, by 2:

Group the a's:

Subtract 20 from both sides:

Divide both sides by 5:



Now we can substitute a back into our "modified" Equations 2 & 3 to solve for b & c:
Equation 2:


Equation 3:




So our angles are 140, 70 and 150.


Hope this helps. ~ Joe