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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Question 182998: 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 three interior angles of a triangle is always 180 degrees.] What is the measure of each angle? Answer by MathGuyJoe(20) (Show Source):
You can put this solution on YOUR website! 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:
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