find the value of each variable.
$x = $
$y = $
$z = $

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Pair Theorem", "Linear Equations" ], "new_concepts": [ "Consecutive Interior Angles Theorem", "Alternate Interior Angles Theorem" ], "current_concepts": [ "Linear Pair Theorem", "Linear Equations", "Consecutive Interior Angles Theorem", "Alternate Interior Angles Theorem" ] } ## Find the value of x using the Linear Pair Theorem $$ \begin{aligned} x + 110 &= 180 \ x &= 70 \end{aligned} $$ ## Find the value of y using the Alternate Interior Angles Theorem $$ \begin{aligned} y &= x \ y &= 70 \end{aligned} $$ ## Find the value of z using the Consecutive Interior Angles Theorem $$ \begin{aligned} z + 90 &= 180 \ z &= 90 \end{aligned} $$ Find the value of each variable. $x =$ 70 $y =$ 70 $z =$ 90 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines and Transversals" ] }

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Question

Explanation:

Find the value of x using the Linear Pair Theorem

Find the value of y using the Alternate Interior Angles Theorem

Find the value of z using the Consecutive Interior Angles Theorem

Answer: