find the measure of the arc.

(m\widehat{efd} = \ ?\ ^{\circ})

Question

find the measure of the arc.

(m\widehat{efd} = \ ?\ ^{\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": [ "Arc Measure", "Central Angle Theorem" ], "new_concepts": [], "current_concepts": [ "Arc Measure", "Central Angle Theorem", "Angles around a Point" ] } ## Identify the given angles Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &\angle CDE = 90^\circ \quad (\text{indicated by the right-angle symbol})\ &\angle EDF = 146^\circ \end{aligned} $$ ## Calculate the remaining central angle Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &\angle FDC = 360^\circ - (\angle CDE + \angle EDF)\ &\angle FDC = 360^\circ - (90^\circ + 146^\circ) = 124^\circ \end{aligned} $$ ## Determine the measure of the major arc EFD Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &m\widehat{EFD} = 360^\circ - m\widehat{ED}\ &m\widehat{EFD} = 360^\circ - 90^\circ = 270^\circ \end{aligned} $$ Find the measure of the arc. $m\widehat{EFD} =$ 270$^\circ$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Arc Measure" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given angles

Calculate the remaining central angle

Determine the measure of the major arc EFD

Answer: