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Chapter 10: Problem 25

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

Short Answer

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

Step by step solution

01

Identify the number of sides

In this problem, the number of sides is explicitly mentioned as five. So, \(n = 5\).
02

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 \((5-2) \times 180\).
03

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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 (\

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