11-Arcs and Central Angles - Kuta Software - Infinite Geometry ... - Free Printable

It looks like you've uploaded a worksheet with several geometry problems involving circles, angles, and arcs. Since I can't view images directly, I’ll help you solve the problems based on typical content of such worksheets. Please confirm if this matches your image or provide more details.

Here’s a breakdown of what the problems likely are and how to solve them:

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Problem 1: Name each shaded region

This usually asks you to identify whether a shaded part is:
- A sector (a "slice" of the circle bounded by two radii and an arc)
- A segment (the area between a chord and its arc)
- Or perhaps a semicircle or quadrant

> ✔ Answer:
> - If it's a slice from the center: Sector
> - If it's a curved region bounded by a chord: Segment

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Problem 2: Find the measure of each angle in the given circle

These are typically central angles (angles at the center of the circle). The total degrees in a circle = 360°, so:
- If an angle is labeled as a fraction of the circle (e.g., 1/4), multiply: $ \frac{1}{4} \times 360^\circ = 90^\circ $
- Or if an arc is given, the central angle equals the arc measure.

> ✔ Example:
> If an arc is 120°, then the central angle is also 120°.

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Problem 3: In each figure, name the arc in words. If an arc is a minor arc, write minor; if major, write major

Arcs are named by their endpoints:
- A minor arc is less than 180°
- A major arc is greater than 180°
- A semicircle is exactly 180°

> ✔ Rules:
> - If only two points are labeled (e.g., AB), it's the minor arc AB
> - If three points are used (e.g., ACB), it's the major arc (going the long way)

> ✔ Answer Examples:
> - Arc AB → minor arc
> - Arc ADB → major arc

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Problem 4: Find the measure of the arc or central angle indicated

Use these facts:
- Central angle = arc measure
- Sum of arcs around a circle = 360°
- If an arc is missing, subtract known arcs from 360°
- Inscribed angles are half the arc they intercept

> ✔ Example:
> If a central angle is 60°, then the intercepted arc is 60°.
> If two arcs are 80° and 100°, the third arc is $ 360 - 80 - 100 = 180^\circ $

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Problem 5: Use the diagram to find the measure of each angle

This might involve:
- Inscribed angles: $ \text{Angle} = \frac{1}{2} \times \text{intercepted arc} $
- Tangent-chord angles
- Angles formed by chords intersecting inside/outside the circle

> ✔ Example:
> If an inscribed angle intercepts a 100° arc, then the angle = $ \frac{1}{2} \times 100^\circ = 50^\circ $

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Final Tips:

- Always check whether the angle is central (at center) or inscribed (on circumference).
- Minor arcs < 180°, major arcs > 180°
- Use symmetry and properties of circles (like vertical angles, supplementary angles, etc.)

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If you can describe the specific figures or give the numbers/labels in the image, I can give exact answers for each problem.

For now, here’s a sample completed version based on common problems:

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Sample Answers:

1. Shaded region:
- a) Sector
- b) Segment

2. Angle measures:
- a) 90°
- b) 120°

3. Arc names:
- a) Minor arc AB
- b) Major arc ADB

4. Arc/angle measures:
- a) 70°
- b) 250°

5. Angle measures:
- a) 45° (half of 90° arc)
- b) 135° (supplementary to 45°)

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Let me know the actual values or labels in your image, and I’ll give precise solutions!