Answer :
The central angle of an arc in a circle can be calculated using the formula:
\[ \text{Central Angle} = \left( \frac{\text{Arc Length}}{\text{Circumference}} \right) \times 360^\circ \]
Given that the circumference of the circle is 12 units and the arc length is 88 units, we can plug in these values into the formula:
\[ \text{Central Angle} = \left( \frac{88}{12} \right) \times 360^\circ \]
\[ \text{Central Angle} = 7.33 \times 360^\circ \]
\[ \text{Central Angle} = 263.88^\circ \]
Therefore, the central angle of the arc in the circle is \( 263.88^\circ \).
