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.
A and b are the 2 smaller sides, and c = hypotenus; only for right triangles, Pythagorean Theorem states that: given c = 6 in., a = 2 in. So the three side are 2, 6, and 5.66 inches