which angles are vertical to each other?
$\angle 12$ and $\angle 11$
$\angle 3$ and $\angle 1$
$\angle 1$ and $\angle 7$
$\angle 9$ and $\angle 3$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Vertical Angles" ], "new_concepts": [], "current_concepts": [ "Vertical Angles", "Adjacent Angles", "Linear Pair" ] } ## Identify vertical angles Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\text{Vertical angles are opposite angles formed by intersecting lines.}\ &\text{At the intersection of the diagonal line and the horizontal line:}\ &\angle 1 \text{ and } \angle 3 \text{ are vertical angles.}\ &\angle 2 \text{ and } \angle 4 \text{ are vertical angles.} \end{aligned} $$ ## Evaluate the given options Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\bullet\ \angle 12 \text{ and } \angle 11: \text{Adjacent angles forming a linear pair.}\ &\bullet\ \angle 3 \text{ and } \angle 1: \text{Opposite angles sharing a vertex, which are vertical angles.}\ &\bullet\ \angle 1 \text{ and } \angle 7: \text{Located at different intersections.}\ &\bullet\ \angle 9 \text{ and } \angle 3: \text{Located at different intersections.} \end{aligned} $$

$\angle 12$ and $\angle 11$

$\angle 3$ and $\angle 1$

$\angle 1$ and $\angle 7$

$\angle 9$ and $\angle 3$

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

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Question

Explanation:

Identify vertical angles

Evaluate the given options

Answer: