https://file.aiquickdraw.com/mathbot/file/1730122546689kts8ph0h.jpg

The image shows a circle with center \( M \) and points \( A \), \( B \), \( C \), and \( D \) on its circumference. There is an inscribed angle \( \angle CDA = x \) and another inscribed angle \( \angle CBA = 20^\circ \).

To find the measure of angle \( x \), we can use the fact that angles subtended by the same arc in a circle are equal. Both \( \angle CDA \) and \( \angle CBA \) subtend the same arc \( \overarc{CA} \).

Therefore, \( x = 20^\circ \).

**Answer:** The value of \( x \) is \( 20^\circ \).

Would you like further details or have any other questions?

Here are some related questions to expand on this concept:

1. How do we calculate angles subtended by the same arc in a circle?
2. What is the Inscribed Angle Theorem and how does it apply here?
3. How would the calculation change if the angle \( \angle CBA \) was different?
4. Can we use the same method for angles outside the circle?
5. What are the properties of angles at the center versus angles on the circumference?

**Tip:** In a circle, angles subtended by the same arc at the circumference are always equal.

In the opposite figure, find the angle x.

Learn how to find the measure of an angle subtended by the same arc in a circle. This problem demonstrates the Inscribed Angle Theorem, where angle x is equal to 20°, as both angles subtend the same arc. Suitable for students in Grades 8-10.

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