find the measure of $\angle x$.

$\angle x = \boxed{97}^\circ$

Question

find the measure of $\angle x$.

$\angle x = \boxed{97}^\circ$

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": [], "current_concepts": [ "Vertical Angles", "Triangle Angle Sum Theorem", "Angles on a Straight Line" ] } ## Identify the vertical angles Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\angle \text{interior}_1 = 54^\circ\ &\angle \text{interior}_2 = 29^\circ \end{aligned} $$ ## Apply the triangle angle sum theorem Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} &\angle \text{interior}_3 = 180^\circ - 54^\circ - 29^\circ = 97^\circ \end{aligned} $$ ## Relate to the target angle Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\angle x = \angle \text{interior}_3 = 97^\circ \end{aligned} $$ Find the measure of $\angle x$. $\angle x =$ $97$$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Angle Sum Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertical angles

Apply the triangle angle sum theorem

Relate to the target angle

Answer: