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The sum of two adjacent angles on a straight line is always 180 degrees.
So, we can write the equation: (5x - 28) + (8x) = 180.
Combine like terms: 13x - 28 = 180.
Add 28 to both sides: 13x = 208.
Divide by 13: x = 16.
Now substitute the value of x back into the second angle's measure: (8x) = (8 * 16) = 128.
Therefore, the measure of the second angle is 128°.