Problem 48 - 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 \(16^{\circ}\) more than triple that of its supplement.

Step-by-Step Solution

Answer

The measure of the angle is \(139^{\circ}\).

Step 1: Understand the relationship

First, let \(x\) represent the measure of the unknown angle. Because the problem states that one angle is 16 degrees more than triple its supplement, its supplement can be represented as \(180 - x\). The equation from this relationship is \(x = 3(180 -x) + 16\).

Step 2: Simplify the equation

Next, distribute the 3 in \(3(180 - x)\) to get \(540 - 3x\), giving the new equation \(x = 540 - 3x + 16\).

Step 3: Further Simplify the Equation

Combine the constants \(540 + 16\) to get \(556\), so the equation becomes \(x = 556 - 3x\).

Step 4: Rearrange the Equation to Solve for x

Rearrange the equation by adding \(3x\) to both sides to get \(4x = 556\).

Step 5: Solve for x

Finally, solve for \(x\) by dividing both sides of the equation \(4x = 556\) by \(4\). This gives \(x = 139^{\circ}\).