Problem 45 - 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 \(60^{\circ}\) more than that of its complement.

Step-by-Step Solution

Answer

The measure of the angle is \(75^{\circ}\)

Step 1: Define Variables

Denote the unknown angle as \(x\). Therefore, its complement will be \(90^\circ - x\)

Step 2: Set Up the Equation

Set up the equation based on the given condition: The angle is \(60^\circ\) more than its complement - \(x = 60 + (90 - x)\)

Step 3: Solving for the Unknown

Solve for \(x\) by first simplifying the equation to get \(x = 150 - x\). Add \(x\) to both sides. That will give \(2x = 150\). Then, dividing both sides of the equation by 2 gives \(x = 75\).