Question 1152598
Write an equation for each statement
:
The sum of the measures of the angles of the triangle is 180.
 x + y + z = 180
:
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
:
The third angle is 16 more than the second.
 z = y + 16
-y + z = 16 
:
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
:
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
:
Find y
150 + y + 23 = 180
y = 180 - 173
y = 7 degrees
:
:
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