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The image depicts a circle with a central angle \( \angle AOB \) of \( 100^\circ \). The arc subtended by \( \angle AOB \) is denoted by \( \angle ACB \), which is an inscribed angle.

### Solution:

1. **Understanding the relationship between central and inscribed angles:**
   - The central angle \( \angle AOB \) subtends the same arc as the inscribed angle \( \angle ACB \).
   - The measure of the inscribed angle \( \angle ACB \) is half of the central angle \( \angle AOB \).

2. **Calculating the measure of \( \angle ACB \):**
   \[
   \angle ACB = \frac{1}{2} \times \angle AOB = \frac{1}{2} \times 100^\circ = 50^\circ
   \]

So, the measure of \( \angle ACB \) is \( 50^\circ \).

Would you like further details or have any questions on this? Here are some related questions you might find helpful:

1. What is the relationship between the central angle and an inscribed angle that subtends the same arc?
2. How can you find the measure of an inscribed angle when given the measure of the central angle?
3. What happens to the measure of an inscribed angle when the central angle is \( 180^\circ \)?
4. If the central angle was \( 120^\circ \), what would the inscribed angle be?
5. How does the position of point \( C \) on the circle affect \( \angle ACB \)?

**Tip:** The inscribed angle theorem is a powerful tool in circle geometry. Remember, any angle inscribed in a semicircle is a right angle, which is a special case of this theorem.

The image depicts a circle with a central angle \( \angle AOB \) of \( 100^\circ \). The arc subtended by \( \angle AOB \) is denoted by \( \angle ACB \), which is an inscribed angle.

Explore the relationship between central and inscribed angles in a circle. Learn how to calculate the inscribed angle when the central angle is 100 degrees using the inscribed angle theorem. This problem is ideal for students in Grades 8-10.

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