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Degree Measure of an Angle

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Degree Measure of an Angle

Study Guide

Key Definition

The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. One degree $1^\circ$ is equivalent to a rotation of $\frac{1}{360}$ of a complete revolution.

Important Notes

A complete revolution is $360^\circ$
Half a revolution is $180^\circ$
A quarter of a revolution is $90^\circ$
Angles can be measured using degrees marked on a circle's circumference
Degree measure provides a way to quantify the rotation needed

Mathematical Notation

$360^\circ$ means a complete revolution

$180^\circ$ means half a revolution

$\frac{1}{360}$ represents one degree

$\angle$ denotes an angle

$\sin(\theta)$ is the sine function

Remember to use proper notation when solving problems

Why It Works

Degrees provide a convenient way to measure angles by dividing the circle into 360 equal parts, allowing for precise measurements.

Remember

A full circle is always $360^\circ$, and each degree is a small step towards a complete rotation.

Quick Reference

Complete Revolution:$360^\circ$

Half Revolution:$180^\circ$

Quarter Revolution:$90^\circ$

Understanding Degree Measure of an Angle

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A degree is a measure of rotation, where $360^\circ$ completes a full circle.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is a quarter of a complete revolution?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Calculate the angle for a skateboarder performing a half-pipe trick, which involves a $180^\circ$ rotation.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you perform a three-quarter turn, what is the degree measure of your rotation?

Challenge Quiz

Single Choice Quiz

Advanced

What is the degree measure of an angle that represents two complete revolutions?

Recap

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Review key concepts and takeaways