Central Angle Math Example 1

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Example 1

easy
A central angle in a circle intercepts an arc of 130°130°. What is the measure of the central angle?

Solution

  1. 1
    The Central Angle Theorem states that a central angle (vertex at the centre) is equal in measure to its intercepted arc. This is because both the angle and the arc are defined by the same two radii.
  2. 2
    The intercepted arc measures 130°130°. By the theorem, the central angle = intercepted arc = 130°130°.
  3. 3
    Verify the context makes sense: a central angle of 130°130° means the remaining arc on the other side is 360°−130°=230°360° - 130° = 230°, and the corresponding reflex central angle would be 230°230°. Both arcs and their central angles sum to 360°360° ✓.

Answer

The central angle is 130°130°.
A central angle is an angle whose vertex is at the center of the circle and whose sides are radii. By definition, the central angle and its intercepted arc have the same degree measure. This is the foundational theorem for circle arc-angle relationships.

About Central Angle

An angle whose vertex is at the center of a circle, with its two rays intersecting the circle at two points. Its measure equals the measure of the intercepted arc.

Learn more about Central Angle →

More Central Angle Examples

Example 2 medium

In a circle, three central angles divide the circle into three arcs with measures [formula], [formul

Example 3 easy

A circle is divided into 6 equal sectors. What is the central angle of each sector?

Example 4 hard

In circle [formula], central angle [formula] and central angle [formula]. Find arc [formula] going t

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