what is the measure of angle 2?

- $25^\circ$
- $42^\circ$
- $46^\circ$
- $88^\circ$

Question

what is the measure of angle 2?

- $25^\circ$
- $42^\circ$
- $46^\circ$
- $88^\circ$

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", "Angle Addition Postulate" ] } ## Solve for x using alternate interior angles $$ \begin{aligned} 3x + 17 &= 4x - 8 \ x &= 25 \end{aligned} $$ ## Calculate the measure of the alternate interior angle $$ \begin{aligned} 3x + 17 &= 3(25) + 17 \ &= 92^\circ \end{aligned} $$ ## Calculate the measure of angle 2 $$ \begin{aligned} \angle 2 + 46^\circ + (180^\circ - 92^\circ) &= 180^\circ \ \angle 2 + 46^\circ + 88^\circ &= 180^\circ \ \angle 2 + 134^\circ &= 180^\circ \ \angle 2 &= 46^\circ \end{aligned} $$

25°

42°

46°

88°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines and Transversals" ] }

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QUESTION IMAGE

Question

Explanation:

Solve for x using alternate interior angles

Calculate the measure of the alternate interior angle

Calculate the measure of angle 2

Answer: