Solve Applications with Systems of Equations: example 5.39

Translate to a system of equations and then solve:

The difference of two complementary angles is 26 degrees. Find the measures of the angles.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Translate to a system of equations and then solve:

The difference of two complementary angles is 20 degrees. Find the measures of the angles.

How did it go?

Step 1. Read the problem.
Step 2. Identify what we are looking for.	We are looking for the measure of each angle.
Step 3. Name what we are looking for.	Let $x =$ the measure of the first angle $x =$ . $m =$ the measure of the second angle.
Step 4. Translate into a system of equations.	The angles are complementary. $x + y = 90$
	The difference of the two angles is 26 degrees. $x - y = 26$
The system is	${\begin{matrix} x + y = 90 \\ x - y = 26 \end{matrix}$
Step 5. Solve the system of equations by elimination.	$\begin{matrix} \underset{_________}{{\begin{cases} x + y = 90 \\ x - y = 26 \end{cases}} \\ 2 x = 116 \end{matrix}$
Substitute $x = 58$ into the first equation.	$\begin{matrix} x + y & = & 90 \\ 58 + y & = & 90 \\ y & = & 32 \end{matrix}$
Step 6. Check the answer in the problem. $\begin{matrix} 58 + 32 = 90 ✓ \\ 58 - 32 = 26 ✓ \end{matrix}$
Step 7. Answer the question.	The angle measures are 58 degrees and 42 degrees.

Step 1. Read the problem.
Step 2. Identify what we are looking for.	We are looking for the measure of each angle.
Step 3. Name what we are looking for.	Let $x =$ the measure of the first angle $x =$ . $m =$ the measure of the second angle.
Step 4. Translate into a system of equations.	The angles are complementary. $x + y = 90$
	The difference of the two angles is 26 degrees. $x - y = 26$
The system is	${\begin{matrix} x + y = 90 \\ x - y = 26 \end{matrix}$
Step 5. Solve the system of equations by elimination.	$\begin{matrix} \underset{_________}{{\begin{cases} x + y = 90 \\ x - y = 26 \end{cases}} \\ 2 x = 116 \end{matrix}$
Substitute $x = 58$ into the first equation.	$\begin{matrix} x + y & = & 90 \\ 58 + y & = & 90 \\ y & = & 32 \end{matrix}$
Step 6. Check the answer in the problem. $\begin{matrix} 58 + 32 = 90 ✓ \\ 58 - 32 = 26 ✓ \end{matrix}$
Step 7. Answer the question.	The angle measures are 58 degrees and 42 degrees.