Angle Notation

🏆Practice angle sign

Angle Notation

Angle notation is the way of naming them to know which angle we are referring to. When reading the data, it is customary to mark the given angles and the angle that needs to be found. In this way, we can obtain a better visual image that allows us to find the solution in the most efficient way possible. When we want to demonstrate something or express the angles verbally, we must designate them in a correct and clear manner. Besides, correct notation is important and indispensable to avoid errors.

The main angle symbol:

image of main_angle_symbol

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Test yourself on angle sign !

einstein

Name the angle in the figure below:

AAABBBCCC

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  1. We can name the angle with the letter that defines its vertex.

Notation for angles

We can name the angle with the letter that defines its vertex


2. We can name the angle with the letters with which we denote the segments that form the angle, ensuring that the letter corresponding to the vertex is in the middle.

ensuring that the vertex is in the center

3. We can also name the angle using the vertex letter accompanied by numerical subscripts.

Angles A1 A2


4. Likewise, we can name the angle using Greek letters.

Angles a and B


Remember! The main symbol is:

remember the main angle symbol is


Before almost all notations, we will draw the main symbol. Next comes the name of the angle.
We will start with the notation forms:


The first way of angle notation

We can name the angle with the letter that defines its vertex.
Simply observe which vertex the angle belongs to and write its name next to the main symbol.
When we want to refer to the marked angle, we will indicate it in the following way: 

We can name the angle with the letter that defines its vertex



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The second way of angle notation

We can name the angle with the letters with which we denote the segments that form the angle, ensuring that the letter corresponding to the vertex is in the middle.
What does this mean?
In this example, the indicated angle is formed by the segments AC AC and AB AB , having its vertex at the point A A .
Therefore, we can name it in the following way:

ensuring that the vertex is in the center


As long as the vertex is in the middle of the notation, it will be correct.
You might be wondering why bother and note the three letters?
The answer is quite simple.
In certain cases, we will encounter angles that share a vertex and, to distinguish them, we must use the three-letter notation.
How will we distinguish between the pink angle and the green angle?
We will be forced to use the three-letter notation, ensuring that the vertex always remains in the middle.

How will we distinguish between the pink angle and the green angle

The notation for the pink angle will be:     EBA=ABE∢ EBA = ∢ABE
The notation for the green angle will be: CBE=EBC∢ CBE = ∢EBC


The third way of angle notation

To name angles we can use numbers.
The angle notation will include the name of its vertex and the number noted inside the angle written as a subscript.
Let's see it in the following example:

Let's see it in the following example

The notation for the pink angle will be: A1∢A_1
The notation for the green angle will be: A2∢A_2


Do you know what the answer is?

The fourth way of angle notation

We can also denote the angle using Greek letters.
Examples of Greek letters: 

Alpha Beta Gamma


And we will call them: alpha, beta, and gamma.

Angles a and B

The notation for the pink angle will be: α∢α
The notation for the green angle will be: β∢β


Now you can name an angle in four different ways!

Let's see an example that will summarize the four ways together

No matter which way you choose to denote angles, all are equally correct.
Find out if a specific way is required for notation and if not, simply use the one that is most comfortable for you.


Angle Notation Exercises

Exercise 1

image Exercise 4

Question:

What is the angle?

Answer:

ABC ∢\text{ABC} is equal to 90° 90° .


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Exercise 2

image what type of angle is it

Question:

What type of angle is it?

  1. Right angle
  2. Acute angle
  3. Obtuse angle
  4. Straight angle

Solution:

There are 4 types of angles:

Right angle: equal to 90° 90°

Acute angle: less than 90° 90°

Obtuse angle: greater than 90° 90°

Straight angle: equal to 180° 180°

Answer:

In this case, we are referring to a right angle which is equal to 90° 90°


Exercise 3

Question:

ABC ∢\text{ABC} angle equal to 180° 180°

angle equal to 180°

What type of angle is it?

  1. Right angle
  2. Acute angle
  3. Obtuse angle
  4. Straight angle

Solution:

There are 4 types of angles:

Right angle: equal to 90° 90°

Acute angle: less than 90° 90°

Obtuse angle: greater than 90° 90°

Straight angle: equal to 180° 180°

Answer:

In this case, we are referring to a straight angle which is equal to 180° 180°


Do you think you will be able to solve it?

Exercise 4

Mark the angle of the figure

Task:

Mark the angle of the figure

  1. BDG ∢BDG
  2. DGB ∢DGB
  3. DBG ∢DBG
  4. GBD ∢GBD

Solution:

When marking angles, the middle of the 3 letters represents the vertex of the angle.

Answer:

BDG ∢\text{BDG}


Exercise 5

In triangle ABC, given that AD intersects angle A

In the triangleABC ∆ ABC , given that AD AD , intersects angle A A .

Angle B B is equal to 35° 35° degrees and angle C C is equal to 45° 45° degrees

Task:

Calculate angle A A

Solution:

Given that: B=35° ∢B=35°

Given that: C=45° ∢C=45°

The sum of the angles in the triangle is equal to 180° 180°

(B+C=80°) (B+C=80°)

180(B+C)=100° 180-(B+C)=100°

Given that AD AD cuts angle A A therefore:

CAD+DAB=100° ∢CAD+∢DAB=100°

CAD=100°2=50° ∢CAD=\frac{100°}{2}=50°

Answer:

CAD=100°2=50° ∢CAD=\frac{100°}{2}=50°


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Exercise 6

Given the isosceles triangle ∆ABC.

AB=BC AB=BC

Exercise1 Given the isosceles triangle ABC

Task:

Calculate the angle ∢ABC and write what type it is.

Solve the following exercise:

Solution:

Given the isosceles triangle ABC ∆ ABC AB=BC AB=BC

In the isosceles triangle, the base angles are equal.

Therefore, the angle ABC=45° ∢ABC=45° as well

The sum of the angles of a triangle is equal to 180° 180°

180°45°45°=90° 180°-45°-45°=90°

Answer:

90° 90°


Exercise 7

Given the equilateral triangle ABC

Given the equilateral triangle ABC \triangle ABC

Task:

What is the value of the angle ACB ∢ACB ?

Solution:

Given the equilateral triangle ACB ∆ ACB

In an equilateral triangle, all its angles are 60° 60° .

Therefore, the angle ACB ∢ACB is equal to 60° 60°

Answer:

60° 60°


Do you know what the answer is?

Exercise 8

triangle image ∆ABC

Given the triangle ABC∆ ABC

Angle A=70° ∢A=70°

BC=13 \frac{∢B}{∢C}=\frac{1}{3}

Task:

Calculate the angle C ∢C .

Solution:

We set: α=B∢α = ∢B

Therefore: C=32° ∢C=32°

Given that: BC=13 \frac{∢B}{∢C}=\frac{1}{3}

Given that: A=70°A= 70°

Sum of angles in triangle:

70°+α+3α=180° 70°+α+3α=180°

110°=42° 110°=42° / :4 :4

α=27.5° α=27.5°

Answer:

C=3α=82.5° ∢C=3α=82.5°


Questions on the topic

What are the angle notations?

There are four angle notations: Using the vertex, using three letters, using letters and subscripts, and using Greek letters.

How to find the notation of an angle?

Using the main symbol, followed by one of the existing notations for angles.

What is the correct way to name an angle?

There is no single way and it depends on the notation being used.


Check your understanding

examples with solutions for angle sign

Exercise #1

Name the angle in the figure below:

AAABBBCCC

Video Solution

Step-by-Step Solution

We are looking for an answer where the letter B, which represents the angle in the drawing, is in the middle.

Therefore, answer A is correct since the letter B is in the middle:

ABC ABC

Answer

ABC ∢\text{ABC}

Exercise #2

Name the angle of the figure:

BBBKKKDDD

Video Solution

Step-by-Step Solution

We are looking for an answer where the letter D, which represents the angle in the drawing, is in the middle.

Therefore, answer B is correct since the letter D is in the middle:

BDK BDK

Answer

BDK ∢\text{BDK}

Exercise #3

Mark the angle of the figure:

AAABBBCCC

Video Solution

Answer

ABC ∢\text{ABC}

Exercise #4

Mark the angle of the figure:

GGGDDDBBB

Video Solution

Answer

BDG ∢\text{BDG}

Exercise #5

Mark the angle of the figure:

CCCGGGFFF

Video Solution

Answer

CGF ∢\text{CGF}

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