# Complementary Angles and Systems of Equations

Two angles are complementary of each other. Twice one angle is equal to the other angle plus the product of three and five.

A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.)

B. Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) Scale the graph accordingly; you will need your x-axis and y-axis to go to at least 100.

C. What do you notice about the intersection of the two lines?

D. Solve the system of equations in part A to determine the degrees of each angle by using Gaussian elimination.

Reference

Alexander, D. C., & Koeberlein, G. M. (2003). Elementary geometry for college students (3rd ed.). Boston: Houghton Mifflin.

keywords: compliment, complimentary

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#### Solution Preview

Two angles are complimentary of each other. Twice one angle is equal to the other angle plus the product of three and five.

A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.)

Let the two angles be x and ...

#### Solution Summary

This solution answers four questions about two complementary angles, addressing a system of linear equations, rectangular coordinate systems, intersections and the Gaussian elimination.