<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Angle Classification

Categories of angles based on measurements and relationships.

Atoms Practice
Estimated6 minsto complete
Practice Angle Classification
This indicates how strong in your memory this concept is
Estimated6 minsto complete
Practice Now
Turn In
Angle Classification

Classifying Angles 

By looking at the protractor we measure angles from \begin{align*}0^\circ\end{align*}0 to \begin{align*}180^\circ\end{align*}180. Angles can be classified, or grouped, into four different categories.

Straight Angle: When an angle measures \begin{align*}180^\circ\end{align*}180. The angle measure of a straight line. The rays that form this angle are called opposite rays.

Right Angle: When an angle measures \begin{align*}90^\circ\end{align*}90.

Notice the half-square, marking the angle. This marking is always used to mark right, or \begin{align*}90^\circ\end{align*}90, angles.

Acute Angles: Angles that measure between \begin{align*}0^\circ\end{align*}0 and \begin{align*}90^\circ\end{align*}90.

Obtuse Angles: Angles that measure between \begin{align*}90^\circ\end{align*}90 and \begin{align*}180^\circ\end{align*}180.

It is important to note that \begin{align*}90^\circ\end{align*}90 is NOT an acute angle and \begin{align*}180^\circ\end{align*}180 is NOT an obtuse angle.

Any two lines or line segments can intersect to form four angles. If the two lines intersect to form right angles, we say the lines are perpendicular.

The symbol for perpendicular is \begin{align*}\bot\end{align*}, so these two lines would be labeled \begin{align*}l \bot m\end{align*}lm or \begin{align*}\overleftrightarrow{A C} \bot \overleftrightarrow{D E}\end{align*}ACDE.

There are several other ways to label these two intersecting lines. This picture shows two perpendicular lines, four right angles, four \begin{align*}90^\circ\end{align*}90 angles, and even two straight angles, \begin{align*}\angle ABC\end{align*}ABC and \begin{align*}\angle DBE\end{align*}DBE.




Classifying an Angle 

1. Name the angle and determine what type of angle it is.

The vertex is \begin{align*}U\end{align*}U. So, the angle can be \begin{align*}\angle TUV\end{align*}TUV or \begin{align*}\angle VUT\end{align*}VUT. To determine what type of angle it is, compare it to a right angle. Because it opens wider than a right angle and less than a straight angle it is obtuse.

2. What type of angle is \begin{align*}165^\circ\end{align*}165?

\begin{align*}165^\circ\end{align*}165 is greater than \begin{align*}90^\circ\end{align*}90, but less than \begin{align*}180^\circ\end{align*}180, so it is obtuse.

3. What type of angle is \begin{align*}84^\circ\end{align*}84?

\begin{align*}84^\circ\end{align*}84 is less than \begin{align*}90^\circ\end{align*}90, so it is acute.





Name each type of angle:

Example 1


This angle is exactly \begin{align*}90^\circ\end{align*}90, so it is right.

Example 2

\begin{align*} 67^\circ\end{align*}67

\begin{align*} 67^\circ\end{align*}67 is less than \begin{align*}90^\circ\end{align*}90, so it is acute.

Example 3

\begin{align*} 180^\circ\end{align*}180

This angle is exactly \begin{align*}180^\circ\end{align*}180, so it is straight. 


For exercises 1-5, determine if the statement is true or false.

  1. Two angles always add up to be greater than \begin{align*}90^\circ\end{align*}90.
  2. \begin{align*}180^\circ\end{align*}180 is an obtuse angle.
  3. \begin{align*}180^\circ\end{align*}180 is a straight angle.
  4. Two perpendicular lines intersect to form four right angles.
  5. The measure of a right angle and an acute angle sum to the measure of an obtuse angle.

For exercises 6-11, state what type of angle it is.

  1. \begin{align*}55^\circ\end{align*}55
  2. \begin{align*}92^\circ\end{align*}92
  3. \begin{align*}178^\circ\end{align*}178
  4. \begin{align*}5^\circ\end{align*}5
  5. \begin{align*}120^\circ\end{align*}120
  6. \begin{align*}73^\circ\end{align*}73
  7. Interpret the picture to the right. Write down all equal angles, segments and if any lines are perpendicular.
  8. Draw a picture with the following requirements.

\begin{align*}& AB = BC = BD && m \angle ABD = 90^\circ\\ & m \angle ABC = m \angle CBD && A, B, C \ \text{and} \ D \ \text{are coplanar} \end{align*}

In 14 and 15, plot and sketch \begin{align*}\angle ABC\end{align*}. Classify the angle. Write the coordinates of a point that lies in the interior of the angle.

  1. \begin{align*}A(5, -3), B(-3, -1), C(2, 2)\end{align*}
  2. \begin{align*}A(-3, 0), B(3, 1), C(5, 0)\end{align*}

Review (Answers)

To view the Review answers, open this PDF file and look for section 1.6. 

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More


Acute Angle

An acute angle is an angle with a measure of less than 90 degrees.

Obtuse angle

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.


Perpendicular lines are lines that intersect at a 90^{\circ} angle. The product of the slopes of two perpendicular lines is -1.

Right Angle

A right angle is an angle equal to 90 degrees.

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Angle Classification.
Please wait...
Please wait...