Defining an Angle
An angle is formed when two lines or rays meet at a point. There are also different parts of angles as well as different types of angles. Let’s start with the parts of the angle. As shown in the image, we can see that there are two arms and a vertex when looking at the angle.
We are looking at ∠BCD. The vertex is at point C. This is the point where the lines BC and CD meet. The lines BC and CD are the arms of the angle.
Angles are measured in degrees,radians, minutes and seconds. A degree is represented by the symbol ‘°’. There’s an instrument called the protractor which can be used to measure angles. This instrument is shaped either like a semi-circle or a full circle and has markings to help find the measure of angles.
How do we Name an Angle?
Earlier on in the article we observed that we represented the angle in the image as ∠BCD. The symbol ‘∠’ is used to represent angles. We must note that the vertex is always at the center of representing an angle. However, this will make things confusing in case there is more than one angle with the vertex C as shown in the image.
Here, we can see that ∠C could either be ∠ECD, ∠BCD or ∠BCE. Hence, to avoid any errors we follow the convention of writing angles as ‘∠’ followed by three letters or points of the angle, with the vertex as the center letter. Angles can also be named with numbers or letters by writing a number or letter or even a symbol like the Greek letter ‘𝛳’ as shown in the image.
The angle shown here can be written as ∠BCD or ∠𝛳.
Rapid Recall
Solved Examples
Example 1:
Name the following angles:
Solution:
List the angles:
- ∠ABC – Naming the three points of the angle
- ∠3 – Naming the vertex of the angle
- ∠MNO – Naming the three points of the angle
- ∠EFH, ∠HFG, ∠EFG – Naming the three points and all the angles formed by three lines meeting at a point
- ∠K – Naming the vertex of the angle
Example 2:
Olivia drew three lines meeting at a point. She names the angles formed as just ∠S. Is she right?
Solution:
The angles formed with the vertex S are:
- ∠RST
- ∠RSU
- ∠UST
There are three angles formed at the vertex S, and naming the angles as just ∠S is incorrect as it could mean any of the three angles.
Hence, Olivia is not right in naming the angle as ∠S.
Example 3:
The angle in the image is named by the Greek letter,‘𝚹’. Is this the right way to name the angle?
Solution:
Angles are named with ‘∠’ and the three points of the angle, or the vertex is named.
Hence the angle in the image,∠𝚹, has been named correctly.
In geometry a ray is defined as a line that has a starting point but does not have an ending point and hence, a ray extends to infinity.
A line is defined as a one dimensional figure that extends to infinity in two directions. Lines are straight and do not have any curves or wiggles.
Solid shapes or three dimensional shapes like cubes, cuboids and prisms have many vertices. But not all solid shapes have vertices. Shapes like spheres, hemispheres or cylinders do not have vertices.