Two angles are complementary. The measure of one angle is 60 degrees less than that of the other. Define variables for the measures of the angles. Write equations based on the given facts. Solve the resulting system by elimination to find the measures of the angles.
A) 30 degrees, 60 degrees
B) 60 degrees, 120 degrees
C) 15 degrees, 75 degrees
D) 20 degrees, 80 degrees
E) 150 degrees, 210 degrees

Question

Quizplus · Accepted Answer

Let x be the measure of the first angle and y be the measure of the second angle. The equations are: x + y = 90 (since they are complementary) and x = y - 60. Substituting x = y - 60 into the first equation gives (y - 60) + y = 90, which simplifies to 2y = 150, so y = 75. Then x = 75 - 60 = 15. Thus, the angles are 15 degrees and 75 degrees.

Two Angles Are Complementary