ExplanationThe sector with the greatest central angle will have the greatest area.

Angle BOC is a vertical angle with angle EOF, so BOC also equals 42°.

Angle AOB + angle AOF + angle EOF = 180° (because BE is a straight line).

\(\angle AOB + \angle AOF + \angle EOF =180\)

\(95 + \angle AOF + 42 = 180\)

\(95+ \angle AOF + 42 = 180\)

\(137 + \angle AOF = 180\)

\(\angle AOF = 43\)

Because angle AOF is greater than angle BOC, sector AOF is greater.

Hence option B is correct.
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Sandy

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