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Let's assume that the smaller angle is x degrees and the larger angle (its supplementary angle) is 17x degrees.
Since the sum of the measures of two supplementary angles is 180 degrees, we can write the equation:
x + 17x = 180
18x = 180
x = 10
Therefore, the smaller angle is 10 degrees and the larger angle is 17x = 17 * 10 = 170 degrees.