Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.38

The measure of one angle of a right triangle is 20 degrees more than the measure of the smallest angle. Find the measures of all three 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.

The measure of one angle of a right triangle is 50° more than the measure of the smallest angle. Find the measures of all three angles.

How did it go?

Step 1. Read the problem.
Step 2. Identify what you are looking for.	the measures of all three angles
Step 3. Name. Choose a variable to represent it.	Let $a = 1^{st}$ angle. $a + 20 = 2^{nd}$ angle $90 = 3^{rd}$ angle (the right angle)
Draw the figure and label it with the given information
Step 4. Translate
Write the appropriate formula. Substitute into the formula.
Step 5. Solve the equation.	55 90 third angle
Step 6. Check. $\begin{matrix} 35 + 55 + 90 & ≟ & 180 \\ 180 & = & 180 ✓ \end{matrix}$
Step 7. Answer the question.	The three angles measure 35^°, 55^°, and 90^°.

Step 1. Read the problem.
Step 2. Identify what you are looking for.	the measures of all three angles
Step 3. Name. Choose a variable to represent it.	Let $a = 1^{st}$ angle. $a + 20 = 2^{nd}$ angle $90 = 3^{rd}$ angle (the right angle)
Draw the figure and label it with the given information
Step 4. Translate
Write the appropriate formula. Substitute into the formula.
Step 5. Solve the equation.	55 90 third angle
Step 6. Check. $\begin{matrix} 35 + 55 + 90 & ≟ & 180 \\ 180 & = & 180 ✓ \end{matrix}$
Step 7. Answer the question.	The three angles measure 35^°, 55^°, and 90^°.