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Angles

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Angles

Study Guide

Key Definition

An angle is the union of two rays with a common endpoint called the vertex. The measure of an angle can be given in degrees or radians.

Important Notes

An angle is named using the names of three points; one point on each ray and the vertex.
We can also name an angle using just the vertex, if there is no possibility of confusion.
When three points are used to name an angle, the vertex's name should be the middle letter. For example, ∠BAC is incorrect because the vertex (B) is not in the middle of the notation.
360 degrees is equivalent to $2 \pi$ radians.

Mathematical Notation

$\angle ABC$ refers to the angle formed by the points A, B and C, with B being the vertex.

Remember to use proper notation when solving problems

Why It Works

Angles provide a way to measure rotation and direction. They are fundamental in geometry, trigonometry and many areas of mathematics.

Remember

There are different types of angles: acute (less than 90°), right (exactly 90°), obtuse (greater than 90° and less than 180°), and straight (exactly 180°).

Quick Reference

Acute Angle:$0^\circ < \theta < 90^\circ$

Right Angle:$\theta = 90^\circ$

Obtuse Angle:$90^\circ < \theta < 180^\circ$

Straight Angle:$\theta = 180^\circ$

Understanding Angles

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An angle is formed by two rays that share a common endpoint. This common endpoint is called the vertex of the angle.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the measure of the angle formed by the hands of a clock at 3 o'clock?

Real-World Problem

Question Exercise

Intermediate

Football Kick

A football player kicks a football at an angle of $45^\circ$ with the ground. How acute or obtuse is the complementary angle?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If two angles are complementary and one angle is twice the size of the other, what are the measures of the angles?

Challenge Quiz

Single Choice Quiz

Advanced

How many degrees are in an angle that is $\frac{7}{9}$ of a straight angle?

Recap

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Review key concepts and takeaways