what is the measure of angle 1?

* (86^{\circ})
* (88^{\circ})
* (90^{\circ})
* (92^{\circ})

Question

what is the measure of angle 1?

* (86^{\circ})
* (88^{\circ})
* (90^{\circ})
* (92^{\circ})

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Alternate Interior Angles", "Vertical Angles" ], "new_concepts": [], "current_concepts": [ "Alternate Interior Angles", "Vertical Angles", "Parallel Line Proofs" ] } ## Identify parallel lines and transversal relations $$ \begin{aligned} &L_1 \parallel L_2 \quad \text{(indicated by double red arrows)} \ &\text{Transversal line intersects both parallel lines} \end{aligned} $$ ## Relate given angle to angle 2 $$ \begin{aligned} &\angle 2 \text{ and the angle measuring } 92^\circ \text{ are alternate interior angles} \ &m\angle 2 = 92^\circ \end{aligned} $$ ## Relate angle 2 to angle 1 $$ \begin{aligned} &\angle 1 \text{ and } \angle 2 \text{ are vertical angles} \ &m\angle 1 = m\angle 2 = 92^\circ \end{aligned} $$

(A) $86^\circ$

(B) $88^\circ$

(C) $90^\circ$

(D) $92^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify parallel lines and transversal relations

Relate given angle to angle 2

Relate angle 2 to angle 1

Answer: