Question 1152557: The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of a first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the measures of the first, second and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer.
Found 3 solutions by josgarithmetic, MathTherapy, Alan3354:
Answer by josgarithmetic(39617)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of a first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the measures of the first, second and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer.
We already KNOW this, at least most of us! ====> The sum of the measures of the angles of a triangle is 180.
We don't need to know this, but you should! ===> Do not include the degree symbol in your answer.
From the description, x + y + z = 180 ------ eq (i)
y + z = 3x ----------- eq (ii)
z = y + 15 ----------- eq (iii)
x + 3x = 180 ------ Substituting 3x for y + z in eq (i)
Now you should be able to find the value of x, or the 1st angle
Knowing the value of x, you can substitute that value into eq (ii) to get a value for y + z. This "y + z" value
can then be substituted into eq (i) to get the value of z.
Then, all you'd need to find is the value of y.
Answer by Alan3354(69443)  (Show Source):
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