Question 1152598: The sum of the measures of the angles of the triangle is 180.The sum of the measure of the second and third angles is 5 times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measure of the first, second and third angles respectively. Find the measure of the 3 angles.
Found 3 solutions by ankor@dixie-net.com, MathTherapy, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write an equation for each statement
:
The sum of the measures of the angles of the triangle is 180.
x + y + z = 180
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The sum of the measure of the second and third angles is 5 times the measure of the first angle.
5(y+z) = x
5y + 5z = x
-x + 5y + 5z = 0
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The third angle is 16 more than the second.
z = y + 16
-y + z = 16
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Multiply the 1st equation by 5, subtract the 2nd (rearranged equation)
5x + 5y + 5z = 900
-x + 5y + 5z = 0
---------------------Subtraction eliminates y and z, find z
6x + 0 + 0 = 900
x = 900/6
x = 150 degrees
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Therefore we know y + z = 30 degrees
using this and the last equation
y + z = 30
-y+ z = 16
--------------Addition eliminates y, find z
0 + 2z = 46
z = 46/2
z = 23 degrees
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Find y
150 + y + 23 = 180
y = 180 - 173
y = 7 degrees
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Check this in the statement
"The sum of the measure of the second and third angles is 5 times the measure of the first angle."
5(7 + 23) = 150
5(30) = 150
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! The sum of the measures of the angles of the triangle is 180.The sum of the measure of the second and third angles is 5 times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measure of the first, second and third angles respectively. Find the measure of the 3 angles.
He's wrong. The  .
Answer by josgarithmetic(39617)  (Show Source):
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