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 four times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
+23245 x + y + z = 180
y + z = 4x
z = 12 + y
Combining the first and second equations: x + 4x = 180 ---> 5x = 180 ---> x = 36
Replacing this value into the second equation: y + z = 4(36) ---> y + z = 144
Combining this with the third equation:
y + z = 144
z = 12 + y
---> y + 12 + y = 144
2y = 132
y = 61
---> z = 12 + y = 12 + 61 = 73
But, this is impossible! Where did I make my mistake?
