figure pqrs is a parallelogram. the expressions represent the measures of the angles in degrees.

what is the value of (x)?

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Question

figure pqrs is a parallelogram. the expressions represent the measures of the angles in degrees.

what is the value of (x)?

5
10
20
25

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": [ "Parallelogram Angle Properties", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "Parallelogram Angle Properties", "Solving Linear Equations" ] } ## Identify the geometric relationship Using the *Parallelogram Angle Properties* knowledge point $$ \begin{aligned} &\text{In parallelogram } PQRS\text{, consecutive angles } \angle Q \text{ and } \angle R \text{ are supplementary.}\ &m\angle Q + m\angle R = 180^\circ \end{aligned} $$ ## Set up the equation Using the *Parallelogram Angle Properties* and *Solving Linear Equations* knowledge points $$ \begin{aligned} &(20 + 2x) + 6x = 180 \end{aligned} $$ ## Solve for x Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &20 + 8x = 180\ &8x = 160\ &x = 20 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallelogram Angle Properties" ] }

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Question

Explanation:

Identify the geometric relationship

Set up the equation

Solve for x

Answer: