Angles are everywhere. For example, on a map, you create your route and arrive at a fork in the road. Where the two diverging roads split, a point and angle are formed. The point where the roads diverge is the vertex with the angle separating the area around it. In geometry, this is referred to as the plane. The points inside the angle are the interior part of the angle, and the points that are outside the angle are in the exterior region.
Angles are the most basic building block of triangles and polygons. They are on virtually every page of any geometry book, which means you have to understand what they are and how they work.
Types of Angles
In geometry, you are going to encounter five basic angle types. The angle names are as follows:
- Acute angles: These include any angles under 90°. Remember this by thinking “a-cute little angle.” These look like an alligator’s mouth – they don’t open very wide.
- Right angles: These are 90° angles. You are likely familiar with these because they are present in the corners of books, boxes, tabletops, picture frames and all other types of items that you see in day to day life. The lines that create a right angle are considered to be perpendicular.
- Obtuse angles: Angles that measure more than 90°. These are angles that look more like beach or pool chairs and open pretty wide. In fact, these angles look pretty comfortable! After all, they have to be more accommodating than the alligator’s mouth, right?
- Reflex angle: Measures over 180° and is essentially just the other side of a traditional angle. For example, think about the angles present in a traditional triangle. The larger angle is the reflex angle. This is the one that wraps around the corner.
- Straight angle: Straight angles measure 180° but look similar to a line and a point. While this may seem like a weird angle, it is still on this list.
The next step in working with angles is to learn how to use them to determine measurements and other mathematical problems.
Finding a Missing Angle
When trying to fill in missing angles, there are a few things you need to remember.
- The sum of all angles in a triangle will always equal 180°
- The sum of all the angles in a quadrilateral will always equal 360°
With this information, you can easily fill in a missing angle when you know the other two. For example, if you have a triangle where angle A = 47° and angle B = 32°, you can easily solve for angle C with this equation:
A + B + C = 180°
This means that:
47° + 32° + C = 180° All you have to do is solve for C, which equals 101°. It is that easy to determine missing angles.
The fact is, working with angles is much easier than most people think. When you know the basics, you can easily solve for any missing angle that may be present. Take the time to learn the types of angles, and you can easily solve basic problems with this information.