Question

The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.

Answer 1

Let "b" be the measure of the second angle.

Since the sum of the two complementary angles is 90°, the first angle must measure 90° - b.

The given information is that the measure of the first angle is 15 less than twice the measure of the second angle:

a = 2b - 15

We now have two equations:

a + b = 90

a = 2b - 15

This system of two equations can be used to determine the measures of both angles, a and b.