given that point $z$ is the incenter of the triangle, $\angle xwy = 75^{\circ}$, and $\angle wyx = 50^{\circ}$, determine the measure of $\angle zxy$.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Triangle Angle Sum Theorem", "Incenter Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Angle Sum Theorem", "Incenter Theorem", "Angle Bisector Theorem" ] } ## Calculate the third interior angle of the triangle $$ \begin{aligned} \angle WXY &= 180^\circ - \angle XWY - \angle WYX \ \angle WXY &= 180^\circ - 75^\circ - 50^\circ \ \angle WXY &= 55^\circ \end{aligned} $$ ## Determine the measure of the bisected angle $$ \begin{aligned} \angle ZXY &= \frac{1}{2} \angle WXY \ \angle ZXY &= \frac{1}{2} (55^\circ) \ \angle ZXY &= 27.5^\circ \end{aligned} $$ $27.5^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Incenter Theorem" ] }

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Calculate the third interior angle of the triangle

Determine the measure of the bisected angle

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