Angle Notation

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

Notation for angles

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.

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

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

Remember! The main symbol is:

If you are interested in learning more about other angle topics, you can enter one of the following articles:

• Scientific notation of numbers
• Sides, vertices, and angles
• Bisector
• Right angle
• Acute angle
• Obtuse angle
• Plane angle
• Adjacent angles
• Vertically opposite angles
• Alternate angles
• Corresponding angles
• Sum of the angles of a triangle
• Sum of the angles of a polygon
• Sum and difference of angles

In the blog of Tutorela you will find a variety of articles about mathematics.

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

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 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 $AC$ and $AB$, having its vertex at the point $A$.
Therefore, we can name it in the following way:

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.

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

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:

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

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

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

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

Now you can name an angle in four different ways!

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.

Question:

What is the angle?

Answer:

$∢\text{ABC}$ is equal to $90°$.

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 $90°$

Acute angle: less than $90°$

Obtuse angle: greater than $90°$

Straight angle: equal to $180°$

Answer:

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

Question:

$∢\text{ABC}$ 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 $90°$

Acute angle: less than $90°$

Obtuse angle: greater than $90°$

Straight angle: equal to $180°$

Answer:

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

Task:

Mark the angle of the figure

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

Solution:

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

Answer:

$∢\text{BDG}$

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

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

Task:

Calculate angle $A$

Solution:

Given that: $∢B=35°$

Given that: $∢C=45°$

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

$(B+C=80°)$

$180-(B+C)=100°$

Given that $AD$ cuts angle $A$ therefore:

$∢CAD+∢DAB=100°$

$∢CAD=\frac{100°}{2}=50°$

Answer:

$∢CAD=\frac{100°}{2}=50°$

Given the isosceles triangle ∆ABC.

$AB=BC$

Task:

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

Solve the following exercise:

Solution:

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

In the isosceles triangle, the base angles are equal.

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

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

$180°-45°-45°=90°$

Answer:

$90°$

Given the equilateral triangle $\triangle ABC$

Task:

What is the value of the angle $∢ACB$?

Solution:

Given the equilateral triangle $∆ ACB$

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

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

Answer:

$60°$

Given the triangle $∆ ABC$

Angle $∢A=70°$

$\frac{∢B}{∢C}=\frac{1}{3}$

Task:

Calculate the angle $∢C$.

Solution:

We set: $∢α = ∢B$

Therefore: $∢C=32°$

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

Given that: $A= 70°$

Sum of angles in triangle:

$70°+α+3α=180°$

$110°=42°$ / $:4$

$α=27.5°$

Answer:

$∢C=3α=82.5°$

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.