What if you wanted to group different angles into different categories? After completing this Concept, you'll be able to classify angles geometrically.
By looking at the protractor we measure angles from to . Angles can be classified, or grouped, into four different categories.
Straight Angle: When an angle measures . The angle measure of a straight line. The rays that form this angle are called opposite rays.
Right Angle: When an angle measures .
Notice the half-square, marking the angle. This marking is always used to mark right, or , angles.
Acute Angles: Angles that measure between and .
Obtuse Angles: Angles that measure between and .
It is important to note that is NOT an acute angle and 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 , so these two lines would be labeled or .
There are several other ways to label these two intersecting lines. This picture shows two perpendicular lines, four right angles, four angles, and even two straight angles, and .
Name the angle and determine what type of angle it is.
The vertex is . So, the angle can be or . 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.
What type of angle is ?
is greater than , but less than , so it is obtuse.
What type of angle is ?
is less than , so it is acute.
Watch this video for help with the Examples above.
A straight angle is when an angle measures . A right angle is when an angle measures . Acute angles are angles that measure between and . Obtuse angles are angles that measure between and . If two lines intersect to form right angles, the lines are perpendicular.
Name each type of angle:
For exercises 1-5, determine if the statement is true or false.
- Two angles always add up to be greater than .
- is an obtuse angle.
- is a straight angle.
- Two perpendicular lines intersect to form four right angles.
- A right angle and an acute angle make an obtuse angle.
For exercises 6-11, state what type of angle it is.
- Interpret the picture to the right. Write down all equal angles, segments and if any lines are perpendicular.
- Draw a picture with the following requirements.
In 14 and 15, plot and sketch . Classify the angle. Write the coordinates of a point that lies in the interior of the angle.