this circle is already partitioned.

determine the measure of the highlighted central angle.

radians | degrees

explain your thinking.

Question

this circle is already partitioned.

determine the measure of the highlighted central angle.

radians | degrees

explain your thinking.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radian to Degree Conversion", "Trigonometric Angles" ], "new_concepts": [ "Central Angle of Partitioned Circle" ], "current_concepts": [ "Radian to Degree Conversion", "Trigonometric Angles", "Central Angle of Partitioned Circle" ] } ## Count the total partitions and highlighted sectors $$ \begin{aligned} &\text{Total sectors in circle} = 16\ &\text{Highlighted sectors} = 4 \end{aligned} $$ ## Calculate the central angle in radians $$ \begin{aligned} &\theta_{\text{rad}} = 2\pi \times \frac{4}{16} = \frac{\pi}{2} \end{aligned} $$ ## Convert the central angle to degrees $$ \begin{aligned} &\theta_{\text{deg}} = 360^\circ \times \frac{4}{16} = 90^\circ \end{aligned} $$ | Radians | Degrees | |---|---| | $\frac{\pi}{2}$ | $90^\circ$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Central Angle of Partitioned Circle" ] }

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QUESTION IMAGE

Question

Explanation:

Count the total partitions and highlighted sectors

Calculate the central angle in radians

Convert the central angle to degrees

Answer: