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The problem asks for the sum of the measures of the angles of a **pentagonal prism**.

A pentagonal prism has two pentagonal bases and five rectangular lateral faces. To clarify, the question likely refers to the **sum of the interior angles of the pentagonal base**, since prisms themselves do not have a well-defined total "angle sum" in 3D space, but polygons do.

### Sum of the angles of a pentagon:
For any polygon, the sum of the interior angles can be calculated using the formula:
\[
\text{Sum of angles} = (n - 2) \times 180^\circ
\]
where \(n\) is the number of sides.

For a **pentagon** (\(n = 5\)):
\[
\text{Sum of angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]

Therefore, the sum of the measures of the angles of the pentagonal base is **540°**.

Let me know if you need further clarification or have additional questions!

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Here are 5 related questions:
1. How can you calculate the sum of angles for a hexagon?
2. What are the interior angles of each angle in a regular pentagon?
3. How is the surface area of a pentagonal prism calculated?
4. What is the volume of a pentagonal prism with known side lengths and height?
5. Can you generalize the angle sum formula for any polygon?

**Tip**: For prisms, focus on their base shapes when asked about angles or interior angle sums.

What is the sum of the measures of the angles of a pentagonal prism?

Discover how to calculate the sum of the interior angles of a pentagon, which forms the base of a pentagonal prism. The formula (n - 2) * 180° helps students in Grades 8-10 understand the geometry of polygons. Explore this practical example and its solution.

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