# 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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 Click here to see ALL problems on Geometric formulas 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: So our angles are 140, 70 and 150. Hope this helps. ~ Joe