if the measure of angle 4 is $132^\circ$, what is the measure of angle 7?

* $32^\circ$
* $48^\circ$
* $132^\circ$
* $148^\circ$

Question

if the measure of angle 4 is $132^\circ$, what is the measure of angle 7?

* $32^\circ$
* $48^\circ$
* $132^\circ$
* $148^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Consecutive Interior Angles", "Vertical Angles" ], "new_concepts": [], "current_concepts": [ "Consecutive Interior Angles", "Vertical Angles", "Parallel Line Proofs" ] } ## Identify the relationship between angle 4 and angle 5 $$ \begin{aligned} &m\angle 4 = 132^\circ \ &m\angle 5 = m\angle 4 = 132^\circ \quad (\text{Alternate Interior Angles}) \end{aligned} $$ ## Relate angle 5 to angle 7 $$ \begin{aligned} &m\angle 5 + m\angle 7 = 180^\circ \quad (\text{Consecutive Interior Angles}) \ &132^\circ + m\angle 7 = 180^\circ \end{aligned} $$ ## Solve for the measure of angle 7 $$ \begin{aligned} &m\angle 7 = 180^\circ - 132^\circ \ &m\angle 7 = 48^\circ \end{aligned} $$

(A) $32^\circ$

(B) $48^\circ$

(C) $132^\circ$

(D) $148^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between angle 4 and angle 5

Relate angle 5 to angle 7

Solve for the measure of angle 7

Answer: