Two complementary angles have measures (4x) degrees and (2x) degrees. What is value of x and the two angle measures?

Since the angles are complementary, their measures add up to 90 degrees. So we have the equation 4x + 2x = 90.

Combining like terms, we get 6x = 90.
Dividing both sides of the equation by 6, we find that x = 15.
Therefore, the measure of the larger angle is 4x = 4 * 15 = 60 degrees, and the measure of the smaller angle is 2x = 2 * 15 = 30 degrees.