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Since the sum of adjacent angles is equal to the resulting angle, we have:
m<1 + m<2 = 135
(2x) + (2x+7) = 135
4x + 7 = 135
4x = 128
x = 32
m<1 = 2x = 2(32) = 64 degrees
m<2 = 2x+7 = 2(32)+7 = 71 degrees
Therefore, the two unknown angle measures are 64 degrees and 71 degrees.