Central Angle Math Example 3

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Example 3

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

Solution

  1. 1
    Step 1: A full circle is 360°360°. If divided into 6 equal sectors, each central angle =360°÷6=60°= 360° \div 6 = 60°.
  2. 2
    Step 2: Each intercepted arc also measures 60°60°.

Answer

Each central angle (and arc) is 60°60°.
Dividing a circle into nn equal sectors gives central angles of 360°n\frac{360°}{n}. For n=6n = 6, each sector has a 60°60° central angle. This is why a regular hexagon can be inscribed in a circle with vertices separated by 60°60° arcs.

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 1 easy

A central angle in a circle intercepts an arc of [formula]. What is the measure of the central angle

Example 2 medium

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

Example 4 hard

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

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