must complete all four challenges for full credit
lines $\overleftrightarrow{te}$ and $\overleftrightarrow{se}$ are tangent to circle $k$.
what is $m\angle tes$ in radians?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Tangent Line to Circle" ], "new_concepts": [ "Tangent Segments from External Point", "Quadrilateral Angle Sum" ], "current_concepts": [ "Tangent Line to Circle", "Trigonometric Angles", "Radian to Degree Conversion" ] } ## Identify the properties of the tangent lines to the circle $$ \begin{aligned} &\angle KTE = \frac{\pi}{2} \text{ rad} \ &\angle KSE = \frac{\pi}{2} \text{ rad} \end{aligned} $$ ## Use the sum of angles in quadrilateral $KSET$ $$ \begin{aligned} &\angle TKS + \angle KTE + \angle TES + \angle KSE = 2\pi \text{ rad} \ &\frac{2\pi}{3} + \frac{\pi}{2} + \angle TES + \frac{\pi}{2} = 2\pi \end{aligned} $$ ## Solve for $m\angle TES$ $$ \begin{aligned} &\frac{2\pi}{3} + \pi + \angle TES = 2\pi \ &\angle TES = \pi - \frac{2\pi}{3} = \frac{\pi}{3} \text{ rad} \end{aligned} $$ $m\angle TES = \frac{\pi}{3}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Tangent Line to Circle" ] }

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Question

Explanation:

Identify the properties of the tangent lines to the circle

Use the sum of angles in quadrilateral \(KSET\)

Solve for \(m\angle TES\)

Answer: