find the measure of $\angle x$.

Question

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": [ "Vertical Angles", "Triangle Angle Sum Theorem" ], "new_concepts": [ "Angles on a Straight Line" ], "current_concepts": [ "Vertical Angles", "Triangle Angle Sum Theorem", "Angles on a Straight Line" ] } ## Identify vertical angles in the intersection Using the *Vertical Angles* knowledge point $$ \text{Vertical angle to } 32^\circ = 32^\circ $$ ## Find the third angle of the triangle Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} &\text{Interior angles sum} = 180^\circ\ &\text{Third angle} = 180^\circ - 55^\circ - 32^\circ = 93^\circ \end{aligned} $$ ## Calculate the measure of angle x Using the *Angles on a Straight Line* knowledge point $$ \begin{aligned} &x + 93^\circ = 180^\circ\ &x = 180^\circ - 93^\circ = 87^\circ \end{aligned} $$ Find the measure of $\angle x$. $x =$ $87^\circ$ { "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 in the intersection

Find the third angle of the triangle

Calculate the measure of angle x

Answer: