Lesson Video: Angles Mathematics

In this video, we will learn how to identify and name angles as acute, right, or obtuse by comparing them visually to a right angle.

08:21

Video Transcript

Angles

In this video, we’re going to learn how to identify and name acute angles, right angles, and obtuse angles.

An angle is the amount of turn between two straight lines or rays, which meet at a vertex or point. We call the sides of an angle the arms. We measure angles in degrees, and this is the symbol we use to write degrees. A complete turn is 360 degrees. And if we make half a turn, we’ve turned 180 degrees. And a quarter of a turn is 90 degrees. Angles which have a square corner, like this angle, are called right angles. A right angle measures 90 degrees. An angle which measures less than 90 degrees is called an acute angle. An angle which measures more than 90 degrees but is less than a straight line is called an obtuse angle.

You could have a go at making some angles of your own. You could use craft pipe cleaners. Which angle have we made? It’s a right angle. Can you see it has a square corner? Which kind of angle is this? It’s less than a right angle. Can you remember its name? It’s an acute angle. This angle is greater than a right angle. Can you remember its name? It’s an obtuse angle. We can tell if an angle is acute or obtuse by comparing it to a right angle.

We can make our own right-angle corner using a piece of paper. And we can use this to check if an angle is less than or greater than a right angle. First, we need to fold the piece of paper in half and then fold it in half again. We’ve made a right-angle measure. We can use our right-angle measure to tell if an angle is greater than or less than a right angle. This angle is greater than a right angle, which means it’s an obtuse angle. By matching the corner of our right-angle measure with the vertex of this angle, we can see the angle measures less than a right angle. So, we know that this is an acute angle because acute angles measure less than a right angle.

Let’s try some questions now to help us practice identifying acute angles, right angles, and obtuse angles.

Determine the type of angle highlighted in orange. Is it a right angle, an obtuse angle, or an acute angle?

In this question, we have to identify the type of angle which is highlighted in orange. Is this angle a right angle? We could use a right-angle measure to check. We simply need to place the corner of our right-angle measure into the corner or vertex of the angle. Now, we can see the orange angle measures more than a right angle. What do we call an angle which is greater than a right angle? Can you remember what an obtuse angle is? This is an obtuse angle. It measures more than a right angle.

The angle highlighted in orange measures more than 90 degrees, so it’s an obtuse angle. Acute angles measure less than a right angle. The type of angle highlighted in orange is an obtuse angle.

Determine the type of angle highlighted in orange. Is it a right angle, an obtuse angle, or an acute angle?

In this question, we have to identify which type of angle the orange angle is. Is this angle a right angle? We’ve drawn the arms of the angle. This is a right angle. The orange angle is less than a right angle. An obtuse angle is an angle which measures greater than 90 degrees. The orange angle is not an obtuse angle. The angle highlighted in orange is an acute angle. It measures less than a right angle. The type of angle highlighted in orange is acute. The orange angle is an acute angle.

Which of these is an acute angle? Angle 𝐴, angle 𝐵, or angle 𝐶.

In this question, we have to identify the acute angle. It can’t be angle 𝐵 because it’s a right angle. This is the symbol we use to show a right angle. We need to use our knowledge of angles to help answer this question. We know that an acute angle is less than a right angle. Does angle 𝐴 or angle 𝐶 measure less than a right angle? We could use a right-angle measure to help. Angle 𝐴 measures less than a right angle. The angle which is an acute angle is angle 𝐴 because it measures less than a right angle. Angle 𝐵 is a right angle, and angle 𝐶 is greater than a right angle. Angle 𝐴 is an acute angle.

Look at the given shape. How many acute angles are there in the shape? How many obtuse angles are there in the shape? How many right angles are there in the shape?

In this question, we have to count the number of acute angles in the given shape, the number of obtuse angles, and the number of right angles. We can answer the third part of the question really quickly. This blue square is the symbol we use to show a right angle, so we know the shape has one right angle. How many acute angles are there? We know acute angles measure less than 90 degrees or less than a right angle. This is an acute angle, and this is an acute angle. Both of these angles measure less than a right angle. This angle is greater than a right angle. We call this type of angle an obtuse angle. So, there are two acute angles, one obtuse angle, and one right angle in the given shape.

What have we learned in this video? We’ve learned how to identify right angles using a right-angle measure. We’ve learned that acute angles measure less than a right angle. And we’ve learned that obtuse angles are greater than a right angle.

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