Problem 47 - Introductory Algebra for College Students

Question

Use the five-step problem-solving strategy to find the measure of the angle described. The angle's measure is three times that of its supplement.

Step-by-Step Solution

Answer

The smaller angle is 45 degrees and the larger angle is 135 degrees.

Step 1: Define the variables

Let's Let \( x \) represent the measure of the smaller angle we're searching for, and \( 3x \) will represent the measure of the other angle, which is said to be three times larger than the smaller one.

Step 2: Set up the equation

Because the problem describes supplementary angles, the sum of their measures is equal to 180 degrees. So, the equation to be solved is \( x + 3x = 180 \).

Step 3: Simplify the equation

The left side of the equation simplifies to \( 4x = 180 \).

Step 4: Solve the equation

To isolate \( x \), divide both sides of the equation by 4. It gives us \( x = 180 / 4 \).

Step 5: Find the value of x and 3x

Solving for \( x \) gives \( x = 45 \) degrees. Substituting the value of \( x \) into the expression for the greater angle, we get \( 3x = 3 * 45 = 135 \) degrees.