find the measure of $\angle x$.

$\angle x = \box^{\circ}$

Question

find the measure of $\angle x$.

$\angle x = \box^{\circ}$

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": [ "Triangle Angle Sum Theorem", "Vertical Angles" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Vertical Angles", "Angles on a Straight Line" ] } ## Identify the vertical angles Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\text{Let the interior angles of the central triangle be } a, b, \text{ and } c.\ &a = 62^\circ \quad (\text{vertical to the given } 62^\circ \text{ angle})\ &b = 29^\circ \quad (\text{vertical to the given } 29^\circ \text{ angle}) \end{aligned} $$ ## Find the third interior angle of the triangle Using the *Triangle Angle Sum Theorem* knowledge point $$ \begin{aligned} &a + b + c = 180^\circ\ &62^\circ + 29^\circ + c = 180^\circ\ &91^\circ + c = 180^\circ\ &c = 89^\circ \end{aligned} $$ ## Determine the measure of angle x Using the *Vertical Angles* knowledge point $$ \begin{aligned} &\angle x \text{ is vertical to the interior angle } c.\ &\angle x = c = 89^\circ \end{aligned} $$ Find the measure of $\angle x$. $\angle x =$ $89$$^\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

Find the third interior angle of the triangle

Determine the measure of angle x

Answer: