Problem 25 - Thinking Mathematically

Question

Find the sum of the measures of the angles of a five-sided polygon.

Step-by-Step Solution

Answer

The sum of the measures of the angles of a five-sided polygon is 540 degrees.

Step 1: Identify the number of sides

In this problem, the number of sides is explicitly mentioned as five. So, \(n = 5\).

Step 2: Apply the formula

Next, apply the formula to calculate the sum of the angles of a polygon. The formula is \((n-2) \times 180\) degrees. Plug in the value of \(n = 5\) into the formula. This gives \((5-2) \times 180\).

Step 3: Calculate the sum

Simplify the expression to get the result. The sum of the measures of the angles of a five-sided polygon is \((3) \times 180 = 540\) degrees.

Key Concepts

Polygon Angle Sum

Understanding the sum of the measures of the angles of a polygon is an essential aspect of geometry. This concept states that the internal angles of a polygon will always add up to a certain measure based on how many sides the polygon has.

Let's delve into the calculation for a five-sided polygon, also known as a pentagon. The general formula to find the sum of the internal angles of any polygon is \[ (n-2) \times 180 \] where \(n\) represents the number of sides of the polygon. For a pentagon (\