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Central Angles

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Central Angles

Study Guide

Key Definition

A central angle is an angle with its vertex located at the center of a circle and its sides containing two radii of the circle. The sum of the measures of the central angles of a circle with no points in common is $360^\circ$.

Important Notes

Central angles divide a circle into sectors, much like slices of pizza.
A pie chart is an example of central angles in action, each slice represented by a different central angle.
The measure of a central angle is equal to the measure of the arc it intersects.

Mathematical Notation

$\angle$ represents an angle.

$360^\circ$ represents the total degrees in a circle.

Remember to use proper notation when solving problems

Why It Works

Central angles work because a circle is a symmetrical shape. All radii of a circle are equal, so the angles they form at the center are consistent.

Remember

Every circle is $360^\circ$. This will always be true, no matter the size of the circle.

Quick Reference

Measure of a Central Angle:The measure of a central angle equals the measure of its intercepted arc.

Understanding Central Angles

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Central angles are simple to understand. Imagine slicing a pizza right down the middle. The angle at the point is a central angle.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the sum of the measures of the central angles in a circle?

Real-World Problem

Question Exercise

Intermediate

Pizza Slice

You're sharing a pizza with three of your friends. If you cut the pizza into four equal slices, what is the measure of the central angle for each slice?

Recap

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