figure tuvs is a parallelogram.
which angles equal 91°?
angles t and v
angles s and u
angles u and v
angles s and t

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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": [ "Properties of Parallelograms", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "Properties of Parallelograms", "Parallelogram Angle Properties", "Solving Linear Equations" ] } ## Identify the relationship between the given angles Using the **Properties of Parallelograms** knowledge point $$ \begin{aligned} &\angle U = (4x + 9)^\circ, \quad \angle V = (6x - 29)^\circ\ &\angle U + \angle V = 180^\circ \end{aligned} $$ ## Solve for x Using the **Solving Linear Equations** knowledge point $$ \begin{aligned} &(4x + 9) + (6x - 29) = 180\ &10x - 20 = 180\ &10x = 200\ &x = 20 \end{aligned} $$ ## Calculate the measures of the angles Using the **Properties of Parallelograms** knowledge point $$ \begin{aligned} &m\angle U = 4(20) + 9 = 89^\circ\ &m\angle V = 6(20) - 29 = 91^\circ\ &m\angle T = m\angle V = 91^\circ\ &m\angle S = m\angle U = 89^\circ \end{aligned} $$ ## Determine which angles equal 91 degrees Using the **Properties of Parallelograms** knowledge point $$ m\angle T = m\angle V = 91^\circ $$

angles T and V

angles S and U

angles U and V

angles S and T

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Properties of Parallelograms" ] }

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Question

Explanation:

Identify the relationship between the given angles

Solve for x

Calculate the measures of the angles

Determine which angles equal 91 degrees

Answer: