find the measure of $\angle x$.
$\angle x = 149^{\circ}$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Vertical Angles", "Supplementary Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Vertical Angles", "Supplementary Angles" ] } ## Identify vertical angles Using the *Vertical Angles* knowledge point $$ \angle \text{interior\_left} = 27^\circ $$ ## Find the third angle of the triangle Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} \angle \text{third} + 58^\circ + 27^\circ &= 180^\circ \ \angle \text{third} + 85^\circ &= 180^\circ \ \angle \text{third} &= 95^\circ \end{aligned} $$ ## Calculate the measure of angle x Using the *Supplementary Angles* knowledge point $$ \begin{aligned} x + 95^\circ &= 180^\circ \ x &= 85^\circ \end{aligned} $$ Find the measure of $\angle x$. $\angle x =$ $85^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Angle Sum Theorem" ] }

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Question

Explanation:

Identify vertical angles

Find the third angle of the triangle

Calculate the measure of angle x

Answer: