Phil incorrectly assumed the exterior angle of a triangle (6x + 24) was the sum of all interior angles. The correct equation is 6x + 24 = 120, yielding x = 16. Phil's error led to an incorrect solution.
Phil's mistake is in assuming that the exterior angle 6x + 24 is equal to the sum of interior opposite angles. However, the correct relationship is that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
The correct equation should be:
6x + 24 = 60 + 60
Phil mistakenly added an extra 60 to the equation. Now, let's solve for x with the correct equation:
6x + 24 = 120
6x = 96
x = 16
So, the correct value of x should be 16. Phil's error was assuming that the exterior angle is the sum of all interior angles instead of just the two non-adjacent interior angles.