Questions: 14) Identify the polygon and find the sum of the measures of the angles.

14) Identify the polygon and find the sum of the measures of the angles.
Transcript text: 14) Identify the polygon and find the sum of the measures of the angles.
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Solution

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Solution Steps

To identify the polygon, we need to determine the number of sides it has. Once we know the number of sides, we can use the formula for the sum of the interior angles of a polygon, which is \((n-2) \times 180\) degrees, where \(n\) is the number of sides.

Step 1: Identify the Polygon

Given that \( n = 5 \), we identify the polygon as a pentagon, which has 5 sides.

Step 2: Calculate the Sum of the Interior Angles

Using the formula for the sum of the interior angles of a polygon, we have: \[ \text{Sum of angles} = (n - 2) \times 180 \] Substituting \( n = 5 \): \[ \text{Sum of angles} = (5 - 2) \times 180 = 3 \times 180 = 540 \]

Final Answer

The sum of the measures of the angles in the polygon is \\(\boxed{540}\\) degrees.

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