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We are given a circle with:

- Radius \( r = 7 \, \text{cm} \)
- Arc length \( AB = 11 \, \text{cm} \)

The task is to find the central angle \( \angle AOB \) in degrees.

We can use the formula for arc length \( s \) to relate the arc and the angle:

\[
s = r \theta
\]

where:
- \( s \) is the arc length,
- \( r \) is the radius,
- \( \theta \) is the angle in radians.

First, solve for \( \theta \):

\[
\theta = \frac{s}{r} = \frac{11 \, \text{cm}}{7 \, \text{cm}} = 1.5714 \, \text{radians}
\]

To convert radians to degrees:

\[
\theta_{\text{degrees}} = \theta \times \frac{180^\circ}{\pi} \approx 1.5714 \times \frac{180^\circ}{3.1416} \approx 90^\circ
\]

Thus, the central angle \( \angle AOB \) is approximately \( 90^\circ \).

Let me know if you'd like more details or have any questions! 

Here are 5 related questions you might want to explore:

1. How would the angle change if the arc length were longer or shorter?
2. Can you derive the formula for the circumference of a circle using this concept?
3. How would you calculate the area of the sector subtended by \( \angle AOB \)?
4. What would the arc length be if \( \angle AOB \) were \( 45^\circ \)?
5. How would you find the length of chord \( AB \)?

**Tip:** Remember that arc length directly depends on both the radius and the angle, so increasing either will increase the arc's length.

If the radius of a circle is 7 cm and the arc length AB is 11 cm, find the measure of the central angle ∠AOB in degrees.

Learn how to calculate the central angle ∠AOB of a circle when the radius is 7 cm and the arc length AB is 11 cm. This problem explores key geometric concepts, including the arc length formula and conversion from radians to degrees. Ideal for students in Grades 9-10.

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