4. SOLVE FOR X:
Using the Alternate Interior Angles Theorem, we know that the 67 degree angle is congruent with the (12x - 5) degree angle. With this information, all I have to do is set the two equal to each other and solve for x.
67 = 12x - 5
67 + 5 = 12x - 5 + 5
72/12 = 12x/12
6 = x
x = 6
SOLVE FOR Y:
Using the Vertical Angles theorem, we know that angle y must be congruent to the 67 degree angle.
y = 67 degrees.
5. SOLVE FOR Y:
Alternate exterior angles: 6(x - 12) = 120
6x - 72 + 72 = 120 + 72
6x/6 = 192/6
x = 32
SOLVE FOR Y:
6((32) - 12) + y = 180
192 - 72 + y = 180
120 + y - 120 = 180 - 120
y = 60
