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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": [ "Vertical Angles", "Alternate Interior Angles", "Corresponding Angles" ], "new_concepts": [], "current_concepts": [ "Vertical Angles", "Alternate Interior Angles", "Corresponding Angles", "Transversal Lines" ] } ## Identify congruent angles at the first intersection $$ \begin{aligned} &m\angle 1 = 45^\circ \ &\angle 1 \text{ and } \angle 4 \text{ are vertical angles} \implies m\angle 4 = m\angle 1 = 45^\circ \end{aligned} $$ ## Identify congruent angles at the second intersection $$ \begin{aligned} &\angle 1 \text{ and } \angle 5 \text{ are corresponding angles} \implies m\angle 5 = m\angle 1 = 45^\circ \ &\angle 4 \text{ and } \angle 5 \text{ are alternate interior angles} \implies m\angle 5 = m\angle 4 = 45^\circ \end{aligned} $$ ## Determine measures of other angles $$ \begin{aligned} &m\angle 2 = 180^\circ - 45^\circ = 135^\circ \ &m\angle 3 = 180^\circ - 45^\circ = 135^\circ \ &m\angle 6 = 180^\circ - 45^\circ = 135^\circ \end{aligned} $$

$\angle 2$

$\angle 3$

$\angle 4$

$\angle 5$

$\angle 6$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Transversal Lines" ] }

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Explanation:

Identify congruent angles at the first intersection

Identify congruent angles at the second intersection

Determine measures of other angles

Answer: