Definition: The angle that an arc makes at the center of the circle of which it is a part.

Try this Drag one of the orange dots that define the endpoints of the blue arc.
Note how the arc angle changes.

One measure of an arc is the angle formed by the arc at the center of the circle that it is a part of. (The other is the length of the arc - see Length of an Arc.) In the figure above, click 'reset' and note that the angle measure of the arc BA is 60°. To see how it derived, click 'Show central angle', and note that the 60° is the angle made by the arc at the center of the circle.

This angle measure is written like this:
and is read as *"the measure of arc AB is 60 degrees".*

When arc angle measures are marked on a diagram, there are two common ways to do it:

1. Write the angle alongside the arc itself. This is less cluttered, but be sure to add the degree mark or it may get confused with the arc length. In the diagram above click 'reset' to see this form. | |

2. You can draw the lines from the arc endpoints to the center point and label the central angle in the usual way. In the diagram above, click 'Show central angle' to see this form. |

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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