Question

if \\(m\angle doc = 44^{\circ}\\) and \\(m\angle cob = 80^{\circ}\\), find the measure of the indicated arc in circle o.

\\(m\widehat{dc} = ?^{\circ}\\)

Explanation:

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

<reasoning>

Identify the given central angle

\[
m\angle DOC = 44^\circ
\]

Apply the central angle theorem

\[
m\widehat{DC} = m\angle DOC
\]

Calculate the arc measure

\[
m\widehat{DC} = 44^\circ
\]
</reasoning>

<answer>
If \(m\angle DOC = 44^\circ\) and \(m\angle COB = 80^\circ\), find the measure of the indicated arc in circle O.

\(m\widehat{DC} =\) <blank>\(44\)</blank>\(^\circ\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Arc Measure"
]
}
</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": [
"Arc Measure",
"Central Angle Theorem"
],
"new_concepts": [],
"current_concepts": [
"Arc Measure",
"Central Angle Theorem"
]
}
</pre_analysis>

<reasoning>

Identify the given central angle

\[
m\angle DOC = 44^\circ
\]

Apply the central angle theorem

\[
m\widehat{DC} = m\angle DOC
\]

Calculate the arc measure

\[
m\widehat{DC} = 44^\circ
\]
</reasoning>

<answer>
If \(m\angle DOC = 44^\circ\) and \(m\angle COB = 80^\circ\), find the measure of the indicated arc in circle O.

\(m\widehat{DC} =\) <blank>\(44\)</blank>\(^\circ\)
</answer>

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