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Answer:

  reflex ∠AOC = 278°

Step-by-step explanation:

You need to know a couple of things to solve this problem:

  • the total number of degrees in a circle is 360°
  • the measure of an inscribed angle is half the measure of the central angle that subtends the same arc
  • the measure of an arc and its central angle are the same.

The second of these means short arc AC is 2×41° = 82°.

The first of these means long arc ABC is 360° -82° = 278°. The central reflex angle AOC subtends the same arc, so has the same measure:

  reflex ∠AOC = 278°

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