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Angle Classification

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Angle Classification

What if you wanted to group different angles into different categories? After completing this Concept, you'll be able to classify angles geometrically.

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CK-12 Foundation: Chapter1AngleClassificationA

James Sousa: Animation of Types of Angles

Guidance

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

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

Right Angle: When an angle measures 90^\circ .

Notice the half-square, marking the angle. This marking is always used to mark right, or 90^\circ , angles.

Acute Angles: Angles that measure between 0^\circ and 90^\circ .

Obtuse Angles: Angles that measure between 90^\circ and 180^\circ .

It is important to note that 90^\circ is NOT an acute angle and 180^\circ 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 \bot , so these two lines would be labeled l \bot m or \overleftrightarrow{A C} \bot \overleftrightarrow{D E} .

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

Example A

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

The vertex is U . So, the angle can be \angle TUV or \angle 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 .

Example B

What type of angle is 165^\circ ?

165^\circ is greater than 90^\circ , but less than 180^\circ , so it is obtuse .

Example C

What type of angle is 84^\circ ?

84^\circ is less than 90^\circ , so it is acute .

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter1AngleClassificationB

Vocabulary

A straight angle is when an angle measures 180^\circ . A right angle is when an angle measures 90^\circ . Acute angles are angles that measure between 0^\circ and 90^\circ . Obtuse angles are angles that measure between 90^\circ and 180^\circ . If two lines intersect to form right angles, the lines are perpendicular .

Guided Practice

Name each type of angle:

1. 90^\circ

2.  67^\circ

3.  180^\circ

Answers:

1. Right

2. Acute

3. Straight

Interactive Practice

Practice

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

  1. Two angles always add up to be greater than 90^\circ .
  2. 180^\circ is an obtuse angle.
  3. 180^\circ is a straight angle.
  4. Two perpendicular lines intersect to form four right angles.
  5. A right angle and an acute angle make an obtuse angle.

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

  1. 55^\circ
  2. 92^\circ
  3. 178^\circ
  4. 5^\circ
  5. 120^\circ
  6. 73^\circ
  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.

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

In 14 and 15, plot and sketch \angle ABC . Classify the angle. Write the coordinates of a point that lies in the interior of the angle.

  1. A(5, -3), B(-3, -1), C(2, 2)
  2. A(-3, 0), B(1, 3), C(5, 0)

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