Question

find \\(m\angle jkn\\) if \\(m\angle nkl = 24^{\circ}\\) and \\(m\angle jkl = 144^{\circ}\\)

\\(m\angle jkn =\\)

Explanation:

<pre_analysis>
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"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
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"concepts_used": [
"Angle Addition Postulate"
],
"new_concepts": [],
"current_concepts": [
"Angle Addition Postulate"
]
}
</pre_analysis>

<reasoning>

State the Angle Addition Postulate relation

\[
m\angle JKN + m\angle NKL = m\angle JKL
\]

Substitute the given values and solve

\[

$$\begin{aligned} m\angle JKN + 24^\circ &= 144^\circ \\ m\angle JKN &= 144^\circ - 24^\circ \\ m\angle JKN &= 120^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find \(m\angle JKN\) if \(m\angle NKL = 24^\circ\) and \(m\angle JKL = 144^\circ\).

\(m\angle JKN =\) <blank>120</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Angle Addition Postulate"
],
"new_concepts": [],
"current_concepts": [
"Angle Addition Postulate"
]
}
</pre_analysis>

<reasoning>

State the Angle Addition Postulate relation

\[
m\angle JKN + m\angle NKL = m\angle JKL
\]

Substitute the given values and solve

\[

$$\begin{aligned} m\angle JKN + 24^\circ &= 144^\circ \\ m\angle JKN &= 144^\circ - 24^\circ \\ m\angle JKN &= 120^\circ \end{aligned}$$

\]
</reasoning>

<answer>
Find \(m\angle JKN\) if \(m\angle NKL = 24^\circ\) and \(m\angle JKL = 144^\circ\).

\(m\angle JKN =\) <blank>120</blank>
</answer>

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