Question

the sum of the measures of the interior angles of a polygon is \\(2880^{\circ}\\). how many sides does the polygon have?

14
16
18
20

Explanation:

<pre_analysis>
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"quality": "clear",
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"skills_matched": [
"step_cot",
"multiple_choice_formatter",
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"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Polygon Interior Angles Theorem",
"Interior Angle Sum Formula"
],
"current_concepts": [
"Polygon Interior Angles Theorem",
"Interior Angle Sum Formula"
]
}
</pre_analysis>

<reasoning>

Set up the interior angle sum equation

\[
(n - 2) \times 180^\circ = 2880^\circ
\]

Solve for n

\[

$$\begin{aligned} n - 2 &= \frac{2880}{180} \\ n - 2 &= 16 \\ n &= 18 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 14</mcq-option>
<mcq-option>(B) 16</mcq-option>
<mcq-correct>(C) 18</mcq-correct>
<mcq-option>(D) 20</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Polygon Interior Angles Theorem"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [],
"new_concepts": [
"Polygon Interior Angles Theorem",
"Interior Angle Sum Formula"
],
"current_concepts": [
"Polygon Interior Angles Theorem",
"Interior Angle Sum Formula"
]
}
</pre_analysis>

<reasoning>

Set up the interior angle sum equation

\[
(n - 2) \times 180^\circ = 2880^\circ
\]

Solve for n

\[

$$\begin{aligned} n - 2 &= \frac{2880}{180} \\ n - 2 &= 16 \\ n &= 18 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 14</mcq-option>
<mcq-option>(B) 16</mcq-option>
<mcq-correct>(C) 18</mcq-correct>
<mcq-option>(D) 20</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Polygon Interior Angles Theorem"
]
}
</post_analysis>