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.

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

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.

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.

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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:

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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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:

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.

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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:

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 $360$.

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 $BOC$

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 $90$.