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Find the measure of an angle whose supplement measures eight times its measure

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The supplement of an angle is basically 180° minus that angle. In other words, two supplementary angles together add up to 180°.

If you let
x be the angle, then
x plus an angle eight times its measure is equal to 180°. Thus,
x + 8x = 180, or
9x = 180. Therefore,
x = 20°.