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Example 5.23 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution
Solve Systems of Equations by Substitution: example 5.23
The measure of one of the small angles of a right triangle is ten more than three times the measure of the other small angle. Find the measures of both 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.
Solution
We will draw and label a figure.
Step 1. Read the problem. Step 2. Identify what you are looking for. We are looking for the measures of the angles. Step 3. Name what we are looking for. Let the measure of the 1st angle
the measure of the 2nd angleStep 4. Translate into a system of equations. The measure of one of the small angles
of a right triangle is ten more than three
times the measure of the other small angle.The sum of the measures of the angles of
a triangle is 180.The system is: Step 5. Solve the system of equations.
We will use substitution since the first
equation is solved for a.Substitute 3b + 10 for a in the
second equation.Solve for b. Substitute b = 20 into the first
equation and then solve for a.Step 6. Check the answer in the problem. We will leave this to you! Step 7. Answer the question. The measures of the small angles are
20 and 70.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
The measure of one of the small angles of a right triangle is 2 more than 3 times the measure of the other small angle. Find the measure of both angles.
How did it go?