if $m\angle boe = 130^{\circ}$ and $m\angle cob = 80^{\circ}$, find the measure of the indicated arc in circle o.

$m\widehat{cbe} = ?^{\circ}$

Question

if $m\angle boe = 130^{\circ}$ and $m\angle cob = 80^{\circ}$, find the measure of the indicated arc in circle o.

$m\widehat{cbe} = ?^{\circ}$

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", "Angle Addition Postulate" ] } ## Identify the given central angles Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &m\angle BOE = 130^\circ\ &m\angle COB = 80^\circ \end{aligned} $$ ## Calculate the measure of the combined central angle Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &m\angle COE = m\angle COB + m\angle BOE\ &m\angle COE = 80^\circ + 130^\circ = 210^\circ \end{aligned} $$ ## Determine the measure of the major arc CBE Using the *Central Angle Theorem* and *Arc Measure* knowledge points $$ \begin{aligned} &m\widehat{CBE} = m\angle COE\ &m\widehat{CBE} = 210^\circ \end{aligned} $$ If $m\angle BOE = 130^\circ$ and $m\angle COB = 80^\circ$, find the measure of the indicated arc in circle O. $m\widehat{CBE} =$ 210$^\circ$ { "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 central angles

Calculate the measure of the combined central angle

Determine the measure of the major arc CBE

Answer: