How to Name Angles: Review Guide for Labeling, Types of Angles & More

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All the angle vocab & naming conventions you need to ace geometry

Co-authored by Dan Hickey Reviewed by Grace Imson, MA

Last Updated: November 27, 2024 Fact Checked

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Ways to Name an Angle

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Types of Angles

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What is an angle?

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Parts of an Angle

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More Angle Vocab

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Getting Help with Angles

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Q&A

Angles are named in two ways. You can name a specific angle by using the vertex point, and a point on each of the angle's rays. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle. You can also name angles by looking at their size. Right angles are 90 degrees. Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees, but less than 180 degrees, which is a straight angle, or a straight line. Using these two naming standards makes it easy to identify and work with angles.

How do you name an angle?

Name a given angle by its vertex and points on each of its arms. For example, call an angle with vertex C and points A and B $\angle ACB$ or $\angle BCA$ . Always list the vertex in the middle of the name. If no other angles share vertex C, you can also simply name the angle $\angle C$ .

Section 1 of 6:

Ways to Name an Angle in Geometry

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1
Label an angle using the vertex and the 2 points on the rays that form its arms. Identify the vertex of the angle, or the point where the line segments or rays that make up the angle meet. Then, identify the endpoints along the rays or line segments that make up the angle’s arms. ^{[1]
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Research source} List these 3 points (with the name of the vertex in the middle) to name the angle. If you are reading the name of an angle, you generally read it from the point on the top ray, to the vertex, to the point on the bottom ray. ^{[2]
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- For example, an angle with vertex C, point A on the top ray, and point B on the bottom ray would be labeled $\angle ACB$ .
- Note: You can also label the angle starting with point B: $\angle BCA$ . As long as the vertex (point C) is listed in the center, the order doesn’t matter.
- Make sure to include the $\angle$ symbol, otherwise it may be confusing to tell whether you’re naming an angle or the triangle that might be formed by the vertex and endpoints.
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Name an angle by its vertex only. Alternatively, leave out the endpoints and simply name the angle for the name of the vertex point. For example, if you have $\angle ACB$ , you could just call it $\angle C$ . ^{[3]
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- Important: This naming convention only works if no other angles share that vertex. For example, if 3 line segments come together at vertex C to form 2 separate angles, simply calling one of them $\angle C$ would be unclear since both angles have a vertex at point C.
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Label an angle by a number or letter. Sometimes, a given angle will be labeled by a letter (usually either a lowercase letter or a Greek letter like $\theta$ ) or a number printed inside the angle. As long as it’s clear which angle the letter or number applies to, you can simply call the angle $\angle f$ , $\angle 4$ , $\angle \theta$ , etc. ^{[4]
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- Often, a short, curved line with arrows on the end will appear with the letter or number to indicate which angle the label applies to.

Section 2 of 6:

Types of Angles in Geometry

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1
Right angle A right angle is created by two perpendicular lines or rays and is exactly 90 degrees. Right angles are often shown by a box in the corner (vertex) of the angle instead of the number 90°. A right angle can be in any orientation as long as the angle measures 90°. ^{[5]
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- Tip: If the measurement of the angle isn’t given, use a protractor to measure it by hand or solve for it using your geometry knowledge .
2
Acute angle Acute angles are less than 90 degrees (0 to 89 degrees.) ^{[6]
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Research source} Unlike a right angle, there is no symbol that denotes an acute angle; the only way to know if an angle is acute is if you measure it or if the measurement is given.
- For example, say $\angle DEF$ measures 40 degrees. Since 40 is less than 90, it is an acute angle.
- Some people remember the definition of an acute angle by thinking of the angle as small and “cute.”
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Obtuse angle . Obtuse angles are between 90 and 180 degrees (91 to 179 degrees). ^{[7]
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Research source} There is no symbol that denotes an obtuse angle.
- For example, say $\angle IHJ$ measures 125 degrees. Since 125 is between 90 and 180, it is an obtuse angle.
- Some people remember the definition of an obtuse angle by thinking of it as being large and “obese.”
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Straight angle A straight angle is a straight line that measures exactly 180 degrees. ^{[8]
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- Note that 180 is half of 360, which is the measurement of a complete turn or circle. So a straight angle is an angle that is open exactly halfway.
- Think of the phrase “Do a 180.” It means to completely turn around (physically or metaphorically), just like how a 180° angle points in 2 perfectly opposite directions.
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Reflex angle A reflex angle is an angle that is greater than 180 degrees but less than 360 degrees. ^{[9]
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Research source} Be careful when identifying these types of angles, because they can look like acute or obtuse angles depending on which way you view the angle opening. ^{[10]
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- Think of an angle opening to a complete rotation. When it is open half way, it is a straight angle. If the angle opens beyond that, it is a reflex angle.
- Take, for example, a right angle. A right angle really makes two angles. One is the 90-degree angle inside the square corner. However, if you think of the angle opening the opposite way, you can see that it could also make a 270-degree angle.
- When 2 angles add up 360 degrees (like a right angle and a 270-degree angle), they are called explementary angles .
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Full rotation A full rotation is 360 degrees, or a full circle. This occurs when an angle opens and makes a complete turn. Full rotations may also be called a “revolution,” “full circle,” or “complete turn.” ^{[11]
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- Think of the phrase “Doing a 360.” It means to turn all the way around once, just like a full rotation.

Section 3 of 6:

What is an angle?

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An angle is the measure of the opening formed when 2 lines intersect at a point. Angles are typically represented by the symbol $\angle$ and can be measured in degrees or radians; both of these measure the circularity or rotation of the angle (AKA, how wide or big the angle is). ^{[12]
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- A full circle can be divided into 360 degrees or 2π radians.

Section 4 of 6:

Parts of an Angle

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An angle is made of a vertex and 2 arms. The arms of the angle are the rays or line segments that intersect each other at a common point. The point where the arms come together is called the vertex . ^{[13]
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- The arms of the angle can be labeled by their endpoints. For example, if you have $\angle XYZ$ where point Y is the vertex, you would have arms labeled $XY$ and $YZ$ .
- You can list the endpoints in either order. For example, $XY$ can also be labeled as $YX$ .
- Arms can be made of rays, lines, or line segments:
  - A ray is a line that extends into infinity in one direction from an endpoint.
  - A line extends into infinity in both directions and has no endpoint.
  - A line segment is a section of a line that has endpoints in either direction.

Section 5 of 6:

More Angle Vocabulary

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1
Pairs of angles Angles are not always isolated and often occur together in pairs (in real life and in geometry problems). Some of these pairs have special relationships and names:
- Complementary angles: Two angles (adjacent or nonadjacent) whose sum is equal to 90°. ^{[14]
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- Supplementary angles: Two angles (adjacent or nonadjacent) whose sum is equal to 180°. ^{[15]
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- Adjacent angles: Two angles that share a common vertex and one common arm, with their non-common arms on either side of the common arm.
- Linear pair: Adjacent angles whose non-common arms form a perfectly straight line (a straight angle). Adjacent supplementary angles for linear pairs.
- Vertical or vertically opposite angles: Congruent angles formed on either side of a common vertex where two lines intersect each other. When this happens, there are two sets of vertical angles that share a vertex (for example, the center of an “X” shape). ^{[16]
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Positive and negative angles Angles can be either positive or negative, depending on the direction of measurement or rotation: ^{[17]
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- Positive angles are measured counterclockwise from the base arm and are most often used to represent angles in geometry. If the base is on the positive X-axis (x), the angle is drawn upward into the positive Y-plane (x, y).
- Negative angles are measured clockwise from the base arm. If the base is on the positive X-axis (x), the angle is drawn downward into the negative Y-plane (x, -y).
- Angles with the base or initial side on the positive X-axis are said to be in standard position .

Section 6 of 6:

Getting Help with Angles

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Ask your math teacher or a tutor for extra help if you’re struggling with angles. Never be afraid to ask for additional help or instruction! If your teacher is unavailable, they will likely have a chart in the classroom that describes the types of angles and shows examples of them. If not, your textbook will explain these, and you can always look for more information online. If you still struggle with angles, consider finding a tutor.
- Some good online resources include Math is Fun , Khan Academy , and CueMath . They offer free study guides and resources, but charge for individual instruction or tutoring.
- To find a tutor, speak to your school counselor or check online resources like WyzAnt or Varsity Tutors .
- When you’re studying angles, math instructor Grace Imson, MA says, “applying [your knowledge] in different cases is very important.” For example, try to label all of the angles in your geometry problems, even if you’re not asked to. This way, you get practice identifying and naming angles in all sorts of different contexts so that you’re prepared for any problem on a test or quiz.

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Question

If you're given only two points (the vertex and one point on one of the rays), is it still possible to name the angle?

Donagan

Top Answerer

No, you wouldn't even have an angle in that case. You have to be able to define two intersecting rays before you have an angle, and it always takes at least two points to define a ray. So you'd need a minimum of three points to make an angle.

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How do I define degree(0)?

Donagan

Top Answerer

In geometry a degree is defined as one-360th of the central angle of a full circle.

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What is an angle of exactly 90 degrees called?

Han

Community Answer

A angle of exactly 90 degrees is a right angle.

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How to Name Angles: Review Guide for Labeling, Types of Angles & More

How do you name an angle?

Steps

Ways to Name an Angle in Geometry

Types of Angles in Geometry

What is an angle?

Parts of an Angle

More Angle Vocabulary

Getting Help with Angles

Community Q&A

Tips

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References

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