Question

Two angles are complementary. The measure of a larger angle is six less than three times the measure of the smaller. Find the measures of the two angles. A) (24, 66) B) (27, 63) C) (30, 60) D) (33, 57) E) (36, 54)

Answer 1

The problem can be solved by setting up an equation based on the given information. The two complementary angles in question are 24 degrees and 66 degrees.

Step-by-step explanation:

This problem falls under the category of algebraic word problems. Here's how you solve it: We know that two angles are complementary if the sum of their measures is 90°. Let's call the smaller angle x. According to the problem, the larger angle is 6 less than three times the smaller angle, so we'll call it 3x - 6. To find the values of x and 3x - 6, or the measures of the angles, we'll need to set up an equation based on what we know about complementary angles: x + (3x - 6) = 90. Simplifying this gives 4x = 96, therefore x (the smaller angle) equals 24. This makes the larger angle 3x - 6 which equals 66. Therefore, the two angles are 24° and 66°, which aligns with choice A) (24, 66).

Learn more about Complementary Angles