Types of angles (right, acute, obtuse, straight)

Acute angle - greater than 0 and less than 90

Illustration of an acute angle, measuring less than 90 degrees. The angle is highlighted in orange, emphasizing its small size. A black curved arc marks the interior of the angle, visually representing the measure

Right angle - equals 90

Diagram of a right angle, measuring exactly 90 degrees. The two perpendicular orange lines form a perfect L-shape, with a small black square in the corner indicating the right angle property.

Obtuse angle - greater than 90 and less than 180

Diagram of an obtuse angle, measuring greater than 90 degrees but less than 180 degrees. The two orange lines form an open angle, with a black arc marking the angle measurement.

Straight angle - equals 180

Diagram of a straight angle, measuring exactly 180 degrees. A vertical orange line intersects a black semicircle, illustrating the concept of a straight angle in geometry.

Detailed explanation

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Test yourself on types of aangles (right, acute, obtuse, flat)!

$∢\text{ABC}$ equal to 90°.

What angle is it?

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Types of Angles (Right, Acute, Obtuse, Straight)

First, it's important to remember that a complete angle is 360 degrees.
360 degrees means that the angle makes a complete rotation on the line. Let's see this in the illustration.

Illustration of a full rotation angle, also known as a complete angle or 360-degree angle. A black dot at the center represents the vertex, with an orange circular arrow indicating a full turn around the point.

Now that we remember what a complete angle is, let's move on to the other types of angles.

acute angle

An acute angle is an angle whose size is between $0$ and $90$ non-inclusive. In other words, greater than $0$ but less than $90$ .
Let's look at examples of an acute angle:

As you can see, an acute angle can be any angle between $0$ and $90$ not inclusive.

How will we remember what an acute angle is?

When something is sharp it is usually small and pointy. Similarly, an acute angle is the smallest among other angles. Greater than $0$ but less than $90$ degrees.

Click here to learn more about acute angle.

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Test your knowledge

Question 1

What type of angle is

$∢\text{ABC}$ ?

Question 2

$∢\text{ABC}$ is an angle measuring less than 90°.

What kind of angle angle is it?

Question 3

Which figure depicts a right angle?

right angle

A right angle is an angle that equals $90$ degrees.
It is made up of two lines that are completely straight, so in your imagination, you can add $2$ more lines to create a rectangle or a square.
Its symbol is also always made up of two straight lines.
Let's look at examples of a right angle:

How will we remember what a right angle is?

The right angle equals $90$ degrees and is found between two perfectly straight lines arranged in an aesthetic way. All you need to remember here is that a right angle equals $90$ degrees.

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obtuse angle

An obtuse angle is an angle between $90$ degrees and $180$ degrees, not inclusive. In other words, it's an angle that is larger than a right angle but smaller than a straight angle.
Let's look at some examples of obtuse angles:

How will we remember what an obtuse angle is?

The truth is that the easiest way to remember what an obtuse angle is, is by elimination. Meaning - an acute angle is the small one because it's "sharp", a right angle is 90°, and what's left is the obtuse angle which is the largest among them.

Click here to learn more about obtuse angle

Do you know what the answer is?

Question 1

Which of the following angles are obtuse?

Question 2

Which figure shows a right angle?

Question 3

Which of the following angles is obtuse?

straight angle

A straight angle is an angle of $180$ degrees.
So essentially the 2 rays of the angle lie on a single straight line.
A straight angle is also half of a full angle.
Let's look at examples of a straight angle:

How will we remember what a straight angle is?

Very easily! A straight angle that equals $180$ also looks flat! If you imagine that the lines that make it up are some kind of surface, you'll notice that the straight angle covers the entire surface.
Additionally, it is also half of a complete angle – $180$ is half of $360$ .

And now? Let's practice!

Identify the following angles and determine for each angle whether it is - acute, obtuse, straight or right.
Given - angle $AOB$ equals $90$ degrees.
And segment $AC$ is a straight line.
Check:
angle $AOB$
angle $AC$
angle $AOD$
angle $DOC$
angle $DOB$
angle $BOC$

Diagram of different types of angles formed by intersecting lines labeled A, B, C, D, and O. Includes a right angle marked with a black square. Ideal for math education on angle classification.

Solution:
Angle $AOB$ - Given that this angle equals 90, it is a right angle. Additionally, we can see it has the conventional right angle marking. Generally, we cannot determine that an angle is a right angle without the marking or without stating that it equals $90$ degrees.
Angle $AC$ - Given that segment $AC$ is a straight line, indicating that the entire angle equals $180$ - a straight angle.
Angle $AOD$ - Obtuse angle. We can see it is larger than $90$ based on the angle opposite to it and smaller than $180$ because it is not straight.
Angle $DOC$ - Acute angle. We can see it is smaller than $90$ based on the angle opposite to it.
Angle $DOB$ - Obtuse angle. We can see it consists of a right angle plus an additional part - so it is larger than $90$ .
Angle $BOC$ - Right angle. It complements to 180 with its adjacent angle which is given as $90$ .

Check your understanding

Question 1

Which of the following angles is straight?

Question 2

Which of the following angles is a plane angle?

Question 3

Which of the angles is not an obtuse angle?

Examples with solutions for Types of Aangles (Right, Acute, Obtuse, Flat)

Exercise #1

$∢\text{ABC}$ equal to 90°.

What angle is it?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Step 1: Identify the angle measure provided.
Step 2: Match the angle measure to the corresponding type of angle.
Step 3: Choose the correct type of angle from the multiple-choice options.

Let's break down the process:

Step 1: The problem specifies that $\angle \text{ABC} = 90^\circ$ .

Step 2: Recall the definitions of angle types. A right angle is defined as an angle that measures exactly 90 degrees.

Step 3: Out of the provided choices, select the one that represents a right angle.
- Right angle: $\angle = 90^\circ$ (Correct Choice)
- Acute angle: $\angle < 90^\circ$
- Obtuse angle: $\angle > 90^\circ$ and $\angle < 180^\circ$
- Flat angle: $\angle = 180^\circ$

Thus, the conclusion is that $\angle \text{ABC}$ is a Right angle.

Answer

Right angle

Exercise #2

What type of angle is

$∢\text{ABC}$ ?

Step-by-Step Solution

To determine the type of angle $\angle \text{ABC}$ , we will consider the following:

Step 1: Observe the positions of points A, B, and C, which are depicted in the diagram as lying on a straight line.
Step 2: Recognize that when three points lie on a straight line and a central point (B here) is between two others (A and C), it forms a flat angle.
Step 3: Recall that a flat angle is defined as an angle that measures $180^\circ$ , which is the total rotation a line undergoes around a single point.

Visual inspection of the diagram confirms that points A, B, and C create a straight line. Hence, the angle $\angle \text{ABC}$ must be a flat angle.

Therefore, the angle $\angle \text{ABC}$ is a flat angle.

Answer

Flat angle

Exercise #3

$∢\text{ABC}$ is an angle measuring less than 90°.

What kind of angle angle is it?

Step-by-Step Solution

To determine what kind of angle $\angle \text{ABC}$ is, let's examine the given information: the angle is less than $90^\circ$ .

Step 1: Recall the types of angles based on their measurements:

An acute angle measures less than $90^\circ$ .
A right angle measures exactly $90^\circ$ .
An obtuse angle measures greater than $90^\circ$ but less than $180^\circ$ .
A flat angle measures exactly $180^\circ$ .

Step 2: Match the given information with these definitions.

Since $\angle \text{ABC}$ measures less than $90^\circ$ , it fits the definition of an acute angle.

Therefore, the angle $\angle \text{ABC}$ is an acute angle.

Answer

Acute angle

Exercise #4

Which figure depicts a right angle?

Video Solution

Step-by-Step Solution

A right angle is equal to 90 degrees.

In diagrams (a) and (c), we can observe that the angle symbol is a symbol representing an angle that equals 90 degrees.

Answer

Exercise #5

Which of the following angles are obtuse?

Video Solution

Step-by-Step Solution

By definition, an obtuse angle is an angle that is greater than 90 degrees. We can observe that in one drawing there is an angle of 90 degrees and therefore it is not an obtuse angle, the other two angles are less than 90 degrees meaning they are also not obtuse, they are acute angles.

Therefore, none of the answers is correct.

Answer

None of the options

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Types of angles (right, acute, obtuse, straight)

Types of angles (right, acute, obtuse, straight)

Test yourself on types of aangles (right, acute, obtuse, flat)!

Types of Angles (Right, Acute, Obtuse, Straight)

acute angle

How will we remember what an acute angle is?

right angle

How will we remember what a right angle is?

obtuse angle

How will we remember what an obtuse angle is?

straight angle

How will we remember what a straight angle is?

And now? Let's practice!

Examples with solutions for Types of Aangles (Right, Acute, Obtuse, Flat)

Exercise #1

Step-by-Step Solution

Answer

Exercise #2

Step-by-Step Solution

Answer

Exercise #3

Step-by-Step Solution

Answer

Exercise #4

Video Solution

Step-by-Step Solution

Answer

Exercise #5

Video Solution

Step-by-Step Solution

Answer

More Questions

Types of Aangles (Right, Acute, Obtuse, Flat)