what is the measure of angle 1?

$20^\circ$
$42^\circ$
$138^\circ$
$160^\circ$

Question

what is the measure of angle 1?

$20^\circ$
$42^\circ$
$138^\circ$
$160^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Alternate Exterior Angles", "Parallel Lines and Transversals" ], "new_concepts": [ "Consecutive Interior Angles", "Vertical Angles" ], "current_concepts": [ "Alternate Exterior Angles", "Parallel Lines and Transversals", "Consecutive Interior Angles", "Vertical Angles" ] } ## Set up the equation for x $$ \begin{aligned} (7x - 2)^\circ &= (6x + 18)^\circ \ 7x - 2 &= 6x + 18 \ x &= 20 \end{aligned} $$ ## Calculate the measure of angle 1 $$ \begin{aligned} \text{m}\angle 1 + (7x - 2)^\circ &= 180^\circ \ \text{m}\angle 1 + (7(20) - 2)^\circ &= 180^\circ \ \text{m}\angle 1 + 138^\circ &= 180^\circ \ \text{m}\angle 1 &= 42^\circ \end{aligned} $$

(A) $20^\circ$

(B) $42^\circ$

(C) $138^\circ$

(D) $160^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Set up the equation for x

Calculate the measure of angle 1

Answer: