Angle

Unfortunately, people use the word angle in different ways, so there are 2 definitions for the term angle. This is because you can see an angle with a picture, or describe it with a number.

For example, in the picture above, we have 2 rays and a vertex. These make a picture of an angle.

• Angle: an angle is the figure formed by two rays (or line segments), called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Then what's that little red arc between the two rays? Some would say it's the angle. That's not really true because there would still be an angle even if we didn't draw the little arc. Just think of it as a reminder/warning that we're talking about angles, and we're probably going to need a number to describe how big the angle is.

• Angle: a measure of rotation between two lines. For example, 45°.

So how do you know which angle a question is asking for?

• If the question is talking about a picture, they probably are talking about the first type of angle

• If the question is talking about a number, they probably are talking about the second type of angle

Don't worry about it too much though. If you read the question carefully, you'll know what they want.

For high school geometry, angle measurements usually start at 0° and a full rotation is 360­°. We write a little ∠ symbol in front of the letters to show that we are talking about an angle. It doesn't matter which letter comes first, but what does matter is that the vertex is the middle letter when writing the angle. As you can see in this GeoGebra applet, A is the vertex and it is between B and C in our label.