Question

find the measure of \\(\angle x\\).
\\(\angle x = 149^{\circ}\\)

Explanation:

<pre_analysis>
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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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"needs_drawing": false,
"concepts_used": [
"Triangle Angle Sum Theorem",
"Vertical Angles",
"Supplementary Angles"
],
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"current_concepts": [
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"Vertical Angles",
"Supplementary Angles"
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</pre_analysis>

<reasoning>

Identify vertical angles

Using the Vertical Angles knowledge point
\[
\angle \text{interior\_left} = 27^\circ
\]

Find the third angle of the triangle

Using the Triangle Angle Sum Theorem knowledge point
\[

$$\begin{aligned} \angle \text{third} + 58^\circ + 27^\circ &= 180^\circ \\ \angle \text{third} + 85^\circ &= 180^\circ \\ \angle \text{third} &= 95^\circ \end{aligned}$$

\]

Calculate the measure of angle x

Using the Supplementary Angles knowledge point
\[

$$\begin{aligned} x + 95^\circ &= 180^\circ \\ x &= 85^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find the measure of \(\angle x\).

\(\angle x =\) <blank>\(85^\circ\)</blank>
</answer>

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

Answer:

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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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],
"needs_drawing": false,
"concepts_used": [
"Triangle Angle Sum Theorem",
"Vertical Angles",
"Supplementary Angles"
],
"new_concepts": [],
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"Triangle Angle Sum Theorem",
"Vertical Angles",
"Supplementary Angles"
]
}
</pre_analysis>

<reasoning>

Identify vertical angles

Using the Vertical Angles knowledge point
\[
\angle \text{interior\_left} = 27^\circ
\]

Find the third angle of the triangle

Using the Triangle Angle Sum Theorem knowledge point
\[

$$\begin{aligned} \angle \text{third} + 58^\circ + 27^\circ &= 180^\circ \\ \angle \text{third} + 85^\circ &= 180^\circ \\ \angle \text{third} &= 95^\circ \end{aligned}$$

\]

Calculate the measure of angle x

Using the Supplementary Angles knowledge point
\[

$$\begin{aligned} x + 95^\circ &= 180^\circ \\ x &= 85^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find the measure of \(\angle x\).

\(\angle x =\) <blank>\(85^\circ\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Triangle Angle Sum Theorem"
]
}
</post_analysis>