which angles are vertical to each other?

$\angle 4$ and $\angle 5$
$\angle 8$ and $\angle 2$
$\angle 5$ and $\angle 7$
$\angle 2$ and $\angle 3$

Question

which angles are vertical to each other?

$\angle 4$ and $\angle 5$
$\angle 8$ and $\angle 2$
$\angle 5$ and $\angle 7$
$\angle 2$ and $\angle 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vertical Angles" ], "new_concepts": [], "current_concepts": [ "Vertical Angles", "Linear Pair", "Adjacent Angles" ] } ## Define vertical angles Using the *Vertical Angles* knowledge point Vertical angles are opposite angles formed by two intersecting lines. They share a vertex and are non-adjacent. ## Analyze the given options Using the *Vertical Angles* knowledge point - $\angle 4$ and $\angle 5$: These are interior angles on different vertices. - $\angle 8$ and $\angle 2$: These are on different vertices. - $\angle 5$ and $\angle 7$: These are opposite angles formed by the intersection of the transversal line and the right vertical-like line. They share a vertex and are non-adjacent. - $\angle 2$ and $\angle 3$: These are adjacent angles forming a linear pair. ## Identify the correct pair Using the *Vertical Angles* knowledge point The pair $\angle 5$ and $\angle 7$ are vertical angles.

$\angle 4$ and $\angle 5$

$\angle 8$ and $\angle 2$

$\angle 5$ and $\angle 7$

$\angle 2$ and $\angle 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Vertical Angles" ] }

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QUESTION IMAGE

Question

Explanation:

Define vertical angles

Analyze the given options

Identify the correct pair

Answer: