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To find the measure of the second angle, we can set up an equation since the two angles are supplementary (add up to 180 degrees) as they are on a straight line.
(5x-28) + (8x) = 180
13x - 28 = 180
13x = 208
x = 16
Now we can find the measure of the second angle:
8x = 8 * 16 = 128 degrees
Therefore, the measure of the second angle is 128 degrees.