Angles are formed by intersecting lines or rays. If you take any two lines or rays, will you form at least one angle?

#### Watch This

http://www.youtube.com/watch?v=7iBc5bJdanI James Sousa: Angle Basics

#### Guidance

A **line segment** is a portion of a line with two endpoints. A **ray** is a portion of a line with one endpoint. Line segments are named by their endpoints and rays are named by their endpoint and another point. In each case, a segment or ray symbol is written above the points. Below, the line segment is \begin{align*}\overline{AB}\end{align*}

When two rays meet at their endpoints, they form an **angle**. Depending on the situation, an angle can be named with an angle symbol and by its vertex or by three letters. If three letters are used, the middle letter should be the vertex. The angle below could be called \begin{align*}\angle B\end{align*}

Angles are measured in degrees. You can use a protractor or geometry software to measure angles. Remember that a full circle has \begin{align*}360^\circ\end{align*}

An angle that is exactly \begin{align*}90^\circ\end{align*}**right angle**. A right angle is noted with a little square at its vertex. An angle that is more than \begin{align*}90^\circ\end{align*}**obtuse angle**. An angle that is less than \begin{align*}90^\circ\end{align*}**acute angle**. An angle that is exactly \begin{align*}180^\circ\end{align*}**straight angle**.

Two angles are **complementary** if the sum of their measures is \begin{align*}90^\circ\end{align*}**supplementary** if the sum of their measures is \begin{align*}180^\circ\end{align*}

In the diagram above \begin{align*}\angle AEC\end{align*}**adjacent** **angles** because they are next to each other and share a ray. They are also **supplementary** because together they form a straight angle. \begin{align*}\angle AEC\end{align*}**vertical** **angles**. You can show that vertical angles will always have the same measure.

**Example A**

Explain why you must use three letters to identify any of the angles in the diagram below.

**Solution**: All angles in this diagram have a vertex of \begin{align*}E\end{align*}

**Example B**

\begin{align*}\angle ABC\end{align*}

**Solution:** The “\begin{align*}m\end{align*}

**Example C**

Let \begin{align*}m\angle AEC=x^\circ\end{align*}

**Solution**: If \begin{align*}m\angle AEC=x^\circ\end{align*}

**Concept Problem Revisited**

As long as the lines or rays intersect, at least one angle will be formed. If the lines (or rays) are **parallel**, and therefore **don't intersect**, then no angles will be formed.

#### Vocabulary

A ** line segment** is a portion of a line with two endpoints.

A ** ray** is a portion of a line with one endpoint.

When two rays meet at their endpoints, they form an ** angle**.

An angle that is exactly \begin{align*}90^\circ\end{align*}** right angle**.

An angle that is more than \begin{align*}90^\circ\end{align*}** obtuse angle**.

An angle that is less than \begin{align*}90^\circ\end{align*}** acute angle**.

An angle that is exactly \begin{align*}180^\circ\end{align*}** straight angle**.

Two angles are ** complementary** if the sum of their measures is \begin{align*}90^\circ\end{align*}

Two angles are ** supplementary** if the sum of their measures is \begin{align*}180^\circ\end{align*}

When two lines intersect, ** adjacent angles** are next to each other and share a ray.

**are across from one another and only share a vertex.**

*Vertical angles*#### Guided Practice

1. Name the angle below and classify it by its size.

2. Estimate the measure of the angle from #1. Use a protractor to confirm your answer.

3. What are two lines that form at a right angle called?

**Answers:**

1. \begin{align*}\angle F\end{align*}

2. Remember that exactly half of a right angle is \begin{align*}45^\circ\end{align*}. This angle looks to be more than half of a right angle. You might guess that it is approximately \begin{align*}55^\circ\end{align*}. Using a protractor, you can see that it is about \begin{align*}60^\circ\end{align*}.

#### Practice

1. What's the difference between a line segment, a line, and a ray?

2. Draw an example of a right angle.

3. Draw an example of an obtuse angle.

4. Draw an example of an acute angle.

5. Why are two angles that make a straight angle always supplementary?

6. If \begin{align*}m\angle ABC=(2x+4)^\circ\end{align*}, \begin{align*}m\angle DEF=(3x-5)^\circ\end{align*}, and \begin{align*}\angle ABC\end{align*} and \begin{align*}\angle DEF\end{align*} are complementary, what are the measures of the angles?

7. If \begin{align*}m\angle ABC=(2x+4)^\circ\end{align*}, \begin{align*}m\angle DEF=(3x-5)^\circ\end{align*}, and \begin{align*}\angle ABC\end{align*} and \begin{align*}\angle DEF\end{align*} are supplementary, what are the measures of the angles?

Use the diagram below for #8-#12.

8. Give an example of vertical angles.

9. Give an example of a straight angle.

10. Give an example of supplementary angles.

11. If \begin{align*}m\angle ABC=70^\circ\end{align*}, find \begin{align*}m\angle ABF\end{align*}.

12. If \begin{align*}m\angle ABC=70^\circ\end{align*}, find \begin{align*}m\angle FBG\end{align*}.

13. What do you remember about perpendicular lines?

Use the angle below for #14-#15.

14. Name the angle and classify it based on its size.

15. Estimate the measure of the angle. Use a protractor to confirm your answer.