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To find the value of \( x \) in this problem, we can use the property of an inscribed angle in a circle. Here are the steps:

1. **Identify the inscribed angle and its intercepted arc:**
   - The angle marked \( x^\circ \) is an inscribed angle, which intercepts the arc measuring \( 170^\circ \).

2. **Apply the inscribed angle theorem:**
   - The inscribed angle theorem states that an inscribed angle is half the measure of its intercepted arc. Therefore, the inscribed angle \( x \) is half of \( 170^\circ \).

3. **Calculate \( x \):**
   \[
   x = \frac{170^\circ}{2} = 85^\circ
   \]

Thus, \( x = 85^\circ \).

Would you like further details or have any questions?

Here are five related questions for practice:

1. If an inscribed angle intercepts a \( 120^\circ \) arc, what is the measure of the angle?
2. In a circle, if an inscribed angle measures \( 45^\circ \), what is the measure of its intercepted arc?
3. How does the inscribed angle theorem apply if the angle is a right angle?
4. What is the relationship between an inscribed angle and a central angle that intercept the same arc?
5. How would the problem change if the arc were a minor arc measuring \( 60^\circ \)?

**Tip:** Remember, an inscribed angle in a circle always measures half of the arc it intercepts.

Find the value of x given an inscribed angle in a circle that intercepts an arc measuring 170° and a central angle measuring 60° adjacent to the inscribed angle.

Learn how to find the measure of an inscribed angle x in a circle using the Inscribed Angle Theorem. In this problem, the inscribed angle intercepts an arc of 170°. Suitable for students in Grades 9-10.

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