in the figure below, $\angle 3$ and $\angle 4$ are alternate interior angles.

if $m\angle 3 = (2x - 51)^\circ$ and $m\angle 4 = x^\circ$, what value of $x$ makes $q \parallel r$?

press the hotspot for the value of $x$ that makes the lines parallel and press the answer box to save your selection.

$x = 17$
$x = 51$
$x = 43$
$x = -51$

Question

in the figure below, $\angle 3$ and $\angle 4$ are alternate interior angles.

if $m\angle 3 = (2x - 51)^\circ$ and $m\angle 4 = x^\circ$, what value of $x$ makes $q \parallel r$?

press the hotspot for the value of $x$ that makes the lines parallel and press the answer box to save your selection.

$x = 17$
$x = 51$
$x = 43$
$x = -51$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Converse of the Alternate Interior Angles Theorem", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Converse of the Alternate Interior Angles Theorem", "Linear Equations", "Parallel Lines Cut by a Transversal" ] } ## Relate alternate interior angles for parallel lines Using the *Converse of the Alternate Interior Angles Theorem* knowledge point $$ \begin{aligned} q \parallel r \implies \angle 3 \cong \angle 4 \ m\angle 3 = m\angle 4 \end{aligned} $$ ## Set up the algebraic equation Using the *Linear Equations* knowledge point $$ \begin{aligned} 2x - 51 = x \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} 2x - x = 51 \ x = 51 \end{aligned} $$

$x = 17$

$x = 51$

$x = 43$

$x = -51$

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

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QUESTION IMAGE

Question

Explanation:

Relate alternate interior angles for parallel lines

Set up the algebraic equation

Solve for x

Answer: