A machinist is verifying the angles of a custom part. The part features two complementary angles, and the blueprint specifies that their difference must be 80 degrees. By setting up the system of equations $x + y = 90$ and $x - y = 80$, what are the measures of the two angles?

A carpenter is framing a roof where two rafters must meet at complementary angles. The design requirements state that the difference between these two angles must be 80 degrees. Arrange the following steps in the correct order to solve for the measures of these two angles using the elimination method as described in the course materials.

An HVAC technician is configuring a dual-vent system where two vents must be set at complementary angles. The technical manual requires the difference between these two angles to be ${}80^{\circ}$. Match each value or expression with its corresponding role in determining the exact measurements of these angles.

In a precision machining assembly, two complementary angles are required to have a difference of ${}80^{\circ}$. True or False: The measures of these two angles are ${}85^{\circ}$ and ${}5^{\circ}$.

Angle Measures in Sheet Metal Fabrication

A solar panel installer is adjusting the tilt of a dual-axis tracking mount. The mount uses two complementary angles to maximize solar absorption throughout the day. According to the technical manual, the difference between these two complementary angles must be exactly 80 degrees.

To calculate the specific angles, the installer translates this relationship into the following system of linear equations:

1. $x + y = 90$
2. $x - y = 80$

Using the elimination method, the installer adds these two equations together to eliminate the variable $y$. This step yields the simplified equation: `${}2x$ = ____

Documenting Complementary Joint Angles for Quality Assurance