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Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.34 · Physics Playground

Exercises Word problems and geometry

Example 3.34 from Elementary Algebra, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem

Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.34

The measures of two angles of a triangle are 55 and 82 degrees. Find the measure of the third angle.

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

Step 1. Read the problem. Draw the figure and label it with the given information.
Step 2. Identify what you are looking for.	the measure of the third angle in a triangle
Step 3. Name. Choose a variable to represent it.	Let $x =$ the measure of the angle.
Step 4. Translate.
Write the appropriate formula and substitute.	$m ∠ A + m ∠ B + m ∠ C = 180$
Step 5. Solve the equation.	$\begin{matrix} 55 + 82 + x & = & 180 \\ 137 + x & = & 180 \\ x & = & 43 \end{matrix}$
Step 6. Check. $\begin{matrix} 55 + 82 + 43 & ≟ & 180 \\ 180 & = & 180 ✓ \end{matrix}$
Step 7. Answer the question.	The measure of the third angle is 43 degrees.

Your turn

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

The measures of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.

How did it go?

PreviousSolve Mixture Applications: example 3.33 Next Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.35

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 3.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.