Problem 49 - Introductory Algebra for College Students

Question

Use the five-step problem-solving strategy to find the measure of the angle described. The measure of the angle's supplement is \(10^{\circ}\) more than three times that of its complement.

Step-by-Step Solution

Answer

The measure of the angle is \(95^{\circ}\)

Step 1: Understand the Problem Statement

The problem statement mentions that the measure of the angle's supplement is \(10^{\circ}\) more than three times that of its complement. This means, if the angle is \(x^{\circ}\), its complement is \(90 - x^{\circ}\), and its supplement is \(180 - x^{\circ}\). So, the problem statement in terms of an equation becomes: \(180 - x = 3(90 - x) + 10 \)

Step 2: Simplify the Equation

Solve the equation step by step. First, distribute through the parentheses: \(180 - x = 270 - 3x + 10\). Then, simplify the equation: \(180 - x = 280 - 3x\). Get all terms involving \(x\) on one side by adding \(3x\) and \(x\) on both sides: \(380 = 4x\).

Step 3: Solve for x

You can now solve for \(x\) by dividing both sides of the equation by 4: \(x = 95^{\circ}\).

Step 4: Validate the Answer

The answer should be validated by substituting \(x = 95^{\circ}\) back into the original equation to ensure it holds true. The complement of \(95^{\circ}\) is \(90 - 95 = -5^{\circ}\), and the supplement of \(95^{\circ}\) is \(180 - 95 = 85^{\circ}\). Substituting these values back into the equation, we obtain \(85 = 3(-5) + 10\). After calculation, we find that the left side equals the right side, therefore \(x = 95^{\circ}\) is the correct solution.