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}\\)

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} &m\widehat{CBE} = m\angle COE\\ &m\widehat{CBE} = 210^\circ \end{aligned}$$

\]
</reasoning>

<answer>
If \(m\angle BOE = 130^\circ\) and \(m\angle COB = 80^\circ\), find the measure of the indicated arc in circle O.

\(m\widehat{CBE} =\) <blank>210</blank>\(^\circ\)
</answer>

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"Mathematics",
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</post_analysis>

Answer:

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<reasoning>

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
\[

$$\begin{aligned} &m\widehat{CBE} = m\angle COE\\ &m\widehat{CBE} = 210^\circ \end{aligned}$$

\]
</reasoning>

<answer>
If \(m\angle BOE = 130^\circ\) and \(m\angle COB = 80^\circ\), find the measure of the indicated arc in circle O.

\(m\widehat{CBE} =\) <blank>210</blank>\(^\circ\)
</answer>

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"knowledge_point": [
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