Question

determine the value of \\(x\\) for this equilateral triangle.

\\((2x - 13)^\circ\\)

\\(x = \frac{73}{2}\\)
\\(x = \frac{13}{2}\\)
\\(x = 11\\)
\\(x = 60\\)

Explanation:

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<reasoning>

Identify equilateral triangle properties

\[
\text{An equilateral triangle has three equal interior angles, each measuring } 60^\circ.
\]

Set up the equation for x

\[
2x - 13 = 60
\]

Solve the linear equation

\[

$$\begin{aligned} 2x &= 60 + 13 \\ 2x &= 73 \\ x &= \frac{73}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = \frac{73}{2}\)</mcq-correct>
<mcq-option>(B) \(x = \frac{13}{2}\)</mcq-option>
<mcq-option>(C) \(x = 11\)</mcq-option>
<mcq-option>(D) \(x = 60\)</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Equilateral Triangle Properties"
]
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Answer:

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</pre_analysis>

<reasoning>

Identify equilateral triangle properties

\[
\text{An equilateral triangle has three equal interior angles, each measuring } 60^\circ.
\]

Set up the equation for x

\[
2x - 13 = 60
\]

Solve the linear equation

\[

$$\begin{aligned} 2x &= 60 + 13 \\ 2x &= 73 \\ x &= \frac{73}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = \frac{73}{2}\)</mcq-correct>
<mcq-option>(B) \(x = \frac{13}{2}\)</mcq-option>
<mcq-option>(C) \(x = 11\)</mcq-option>
<mcq-option>(D) \(x = 60\)</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
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"Equilateral Triangle Properties"
]
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