given that point $t$ is the incenter, $\angle qsr = 105^{\circ}$, and $\angle rqs = 35^{\circ}$, determine $\angle srt$.

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Accepted Answer

{ "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" ] } ## Find the third angle of triangle QSR $$ \begin{aligned} \angle QSR + \angle RQS + \angle SRQ &= 180^\circ \ 105^\circ + 35^\circ + \angle SRQ &= 180^\circ \ 140^\circ + \angle SRQ &= 180^\circ \ \angle SRQ &= 40^\circ \end{aligned} $$ ## Apply the incenter property to find angle SRT $$ \begin{aligned} \angle SRT &= \frac{1}{2} \angle SRQ \ \angle SRT &= \frac{1}{2} (40^\circ) \ \angle SRT &= 20^\circ \end{aligned} $$ $20^\circ$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Incenter Theorem" ] }

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Question

Explanation:

Find the third angle of triangle QSR

Apply the incenter property to find angle SRT

Answer: