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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Corresponding Angles", "Parallel Line Proofs" ], "new_concepts": [], "current_concepts": [ "Corresponding Angles", "Parallel Line Proofs" ] } ## Identify the given angles relative to the transversal line $r$ $$ \begin{aligned} &\theta_p = 89^\circ \quad (\text{top-right angle at line } p) \ &\theta_q = 89^\circ \quad (\text{top-right angle at line } q) \ &\theta_u = 91^\circ \quad (\text{top-right angle at line } u) \ &\theta_v = 90^\circ \quad (\text{top-right angle at line } v) \end{aligned} $$ ## Compare corresponding angles to find parallel lines $$ \begin{aligned} &\theta_p = \theta_q = 89^\circ \implies p \parallel q \ &\theta_p eq \theta_u \implies p ot\parallel u \ &\theta_p eq \theta_v \implies p ot\parallel v \end{aligned} $$ ## Determine which lines are parallel to line $p$ $$ \text{Only line } q \text{ is parallel to line } p. $$

only line q

only line r and line v

only line u and line v

only lines q, u, and v

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Proofs" ] }

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Explanation:

Identify the given angles relative to the transversal line \(r\)

Compare corresponding angles to find parallel lines

Determine which lines are parallel to line \(p\)

Answer: