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Angle Classification

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Angle Classification

What if you were given the degree measure of an angle? How would you describe that angle based on its size? After completing this Concept, you'll be able to classify an angle as acute, right, obtuse, or straight.

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CK-12 Classifying an Angle

James Sousa: Animation of Types of Angles

Guidance

Angles can be grouped into four different categories.

Straight Angle: An angle that measures exactly 180^\circ .

Acute Angles: Angles that measure between 0^\circ and up to but not including 90^\circ .

Obtuse Angles: Angles that measure more than 90^\circ but less than 180^\circ .

Right Angle: An angle that measures exactly 90^\circ .

This half-square marks right, or 90^\circ , angles. When two lines intersect to form four right angles, the lines are perpendicular. The symbol for perpendicular is \perp .

Even though all four angles are 90^\circ , only one needs to be marked with the half-square. l \perp m is read line l is perpendicular to line m .

Example A

What type of angle is 84^\circ ?

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

Example B

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 is less than a straight angle, it is obtuse .

Example C

What type of angle is  165^\circ ?

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

CK-12 Classifying an Angle

Guided Practice

Name each type of angle:

1. 90^\circ

2.  67^\circ

3.  180^\circ

Answers

1. Right

2. Acute

3. Straight

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For exercises 1-4, 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.

For exercises 5-10, 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

In exercises 11-15, use the following information: Q is in the interior of \angle ROS . S is in the interior of \angle QOP . P is in the interior of \angle SOT . S is in the interior of \angle ROT and m\angle ROT = 160^\circ, \ m\angle SOT = 100^\circ , and m\angle ROQ = m\angle QOS = m\angle POT .

  1. Make a sketch.
  2. Find m\angle QOP .
  3. Find m\angle QOT .
  4. Find m\angle ROQ .
  5. Find m\angle SOP .

Vocabulary

acute angle

acute angle

An angle that measures between 0^\circ and up to but not including 90^\circ.
obtuse angle

obtuse angle

An angle that measures more than 90^\circ but less than 180^\circ.
perpendicular

perpendicular

When two lines intersect to form four right angles, the lines are perpendicular.
right angle

right angle

An angle that measures exactly 90^\circ.
straight angle

straight angle

An angle that measures exactly 180^\circ.
vertical angles

vertical angles

Two non-adjacent angles formed by intersecting lines.

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