Two angles are complementary. The larger angle is 6° less than thrice the measure of the smaller angle. What is the measure of the larger angle?

Explanation

Solution: Let the measure of the smaller angle be x. Since the angles are complementary, their sum is 90°. Therefore, the measure of the larger angle is 90 - x. According to the problem: The larger angle is 6° less than thrice the measure of the smaller angle: 90 - x = 3x - 6 Now, solve for x: 90 + 6 = 4x 96 = 4x x = 24 The smaller angle is 24°. Now, find the larger angle: Larger angle = 90 - x = 90 - 24 = 66° Answer: The measure of the larger angle is 66°.