Question

matching list

question 4

match the angle pairs with their correct description.

• a pair of angles whose sum of the measures is
• a pair of angles that share a common side and vertex
• a pair of opposite angles formed by intersecting lines
• a pair of angles whose sum of the measures is \\(180^\circ\\)

a. vertical angles
b. adjacent angles
c. supplementary angles
d. complementary angles

Explanation:

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"concepts_used": [
"Supplementary Angles",
"Complementary Angles",
"Vertical Angles",
"Basic Geometry Vocabulary"
],
"new_concepts": [],
"current_concepts": [
"Supplementary Angles",
"Complementary Angles",
"Vertical Angles",
"Basic Geometry Vocabulary"
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}
</pre_analysis>

<reasoning>

Match complementary angles

Using the Complementary Angles and Basic Geometry Vocabulary knowledge points

• The first description is "a pair of angles whose sum of the measures is \(90^\circ\)" (the value \(90^\circ\) is cut off but inferred from the matching option "complementary angles").
• This matches option d. complementary angles.

Match adjacent angles

Using the Basic Geometry Vocabulary knowledge point

• The second description is "a pair of angles that share a common side and vertex".
• This matches option b. adjacent angles.

Match vertical angles

Using the Vertical Angles knowledge point

• The third description is "a pair of opposite angles formed by intersecting lines".
• This matches option a. vertical angles.

Match supplementary angles

Using the Supplementary Angles knowledge point

• The fourth description is "a pair of angles whose sum of the measures is \(180^\circ\)".
• This matches option c. supplementary angles.

</reasoning>

<answer>

Description	Angle Pair
a pair of angles that share a common side and vertex	b. adjacent angles
a pair of opposite angles formed by intersecting lines	a. vertical angles
a pair of angles whose sum of the measures is \(180^\circ\)	c. supplementary angles

</answer>

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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Geometry",
"Basic Geometry Vocabulary"
]
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</post_analysis>

Answer:

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"direct_cot",
"explain_then_answer",
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"concepts_used": [
"Supplementary Angles",
"Complementary Angles",
"Vertical Angles",
"Basic Geometry Vocabulary"
],
"new_concepts": [],
"current_concepts": [
"Supplementary Angles",
"Complementary Angles",
"Vertical Angles",
"Basic Geometry Vocabulary"
]
}
</pre_analysis>

<reasoning>

Match complementary angles

Using the Complementary Angles and Basic Geometry Vocabulary knowledge points

• The first description is "a pair of angles whose sum of the measures is \(90^\circ\)" (the value \(90^\circ\) is cut off but inferred from the matching option "complementary angles").
• This matches option d. complementary angles.

Match adjacent angles

Using the Basic Geometry Vocabulary knowledge point

• The second description is "a pair of angles that share a common side and vertex".
• This matches option b. adjacent angles.

Match vertical angles

Using the Vertical Angles knowledge point

• The third description is "a pair of opposite angles formed by intersecting lines".
• This matches option a. vertical angles.

Match supplementary angles

Using the Supplementary Angles knowledge point

• The fourth description is "a pair of angles whose sum of the measures is \(180^\circ\)".
• This matches option c. supplementary angles.

</reasoning>

<answer>

Description	Angle Pair
a pair of angles that share a common side and vertex	b. adjacent angles
a pair of opposite angles formed by intersecting lines	a. vertical angles
a pair of angles whose sum of the measures is \(180^\circ\)	c. supplementary angles

</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Geometry",
"Basic Geometry Vocabulary"
]
}
</post_analysis>