Question

pentagon

the sum of the measures of the interior angles of a pentagon is \\(\square^{\circ}\\).

Explanation:

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<reasoning>

Identify the polygon type

Using the Polygon Classification knowledge point
A pentagon is a polygon with \(n = 5\) sides.

Apply the interior angle sum formula

The sum of the interior angles of an \(n\)-sided polygon is given by:
\[
S = (n - 2) \times 180^\circ
\]
Substituting \(n = 5\):
\[
S = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]
</reasoning>

<answer>
The sum of the measures of the interior angles of a pentagon is <blank>540</blank>\(^\circ\).
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Polygon Angle Sum"
]
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</post_analysis>

Answer:

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}
</pre_analysis>

<reasoning>

Identify the polygon type

Using the Polygon Classification knowledge point
A pentagon is a polygon with \(n = 5\) sides.

Apply the interior angle sum formula

The sum of the interior angles of an \(n\)-sided polygon is given by:
\[
S = (n - 2) \times 180^\circ
\]
Substituting \(n = 5\):
\[
S = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]
</reasoning>

<answer>
The sum of the measures of the interior angles of a pentagon is <blank>540</blank>\(^\circ\).
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Polygon Angle Sum"
]
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