The sum of the measures of two complementary angles is 90 degrees. If one angle measures
27 degrees more than twice the measure of the other, find the measure of the smaller angle.
Let the smaller angle be x degrees.
Therefore, the larger angle is 2x + 27 degrees.
Since the two angles are complementary, their sum is 90 degrees:
x + 2x + 27 = 90
3x + 27 = 90
3x = 63
x = 21
Therefore, the smaller angle measures 21 degrees.