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Question

the sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angle is five times the measure of the first angle. The third angle is 24 more than the second. Let X, Y, and Z represents the measures of the first, second, and third angle, Respectively. find the measure of three angles

Answer 1

x+y+z=180

y+z=5x

z=y+24

Write these in "standard" form

x+y+z=180

-5x+y+z=0

-y+z=24

Eliminate y by adding the 3rd equation from each of the other 2

x+2z=204

-5x+2z=24

Now eliminate z by subtracting the bottom equation from the top

6x=180

Now go back to the equations and find y and z; then check your work.