Two adjacent angles are on a straight line. One angle has a measure of ( 5x - 28 )° and the other angle has a measure of ( 8x )°. What is the measure of the second angle?

Since the two angles are adjacent and on a straight line, they add up to 180 degrees. We can set up the equation:

(5x - 28) + (8x) = 180

Combining like terms:

13x - 28 = 180

Adding 28 to both sides:

13x = 208

Dividing both sides by 13:

x = 16

Therefore, the second angle has a measure of:

8x = 8 * 16 = <<8*16=128>>128 degrees. Answer: \boxed{128}.