carmen is an engineer making plans to run a rail line, represented by the transversal $t$, through a city.

examine carmens rail plans to identify the measure of $\angle 1$. the streets represented by lines $v$ and $w$ are parallel.

what is the $m\angle 1$?

$25^\circ$
$35^\circ$
$145^\circ$
$155^\circ$

Question

carmen is an engineer making plans to run a rail line, represented by the transversal $t$, through a city.

examine carmens rail plans to identify the measure of $\angle 1$. the streets represented by lines $v$ and $w$ are parallel.

what is the $m\angle 1$?

$25^\circ$
$35^\circ$
$145^\circ$
$155^\circ$

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", "Linear Pair" ], "new_concepts": [], "current_concepts": [ "Alternate Interior Angles", "Linear Pair", "Transversal Lines" ] } ## Identify the alternate interior angle $$ \text{Alternate Interior Angle to } 155^\circ = \angle 2 = 155^\circ $$ ## Use the linear pair relationship to find $m\angle 1$ $$ \begin{aligned} m\angle 1 + m\angle 2 &= 180^\circ \ m\angle 1 + 155^\circ &= 180^\circ \ m\angle 1 &= 180^\circ - 155^\circ \ m\angle 1 &= 25^\circ \end{aligned} $$

(A) 25°

(B) 35°

(C) 145°

(D) 155°

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

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QUESTION IMAGE

Question

Explanation:

Identify the alternate interior angle

Use the linear pair relationship to find \(m\angle 1\)

Answer: