This is an angle. So is this. And even this:
Did you notice what these drawings all have in common? They are all two lines (which are called rays in geometry), that meet at a single point, which is called a vertex.
So in geometric terms, an angle is simply where two intersecting rays share a vertex.
Now you also need to know how to describe angles using symbols and letters-aka geometric notation.
This symbol that looks like an open mouth (∠) denotes an angle. It’s pretty similar to a less than (<) symbol, but sits completely flat.
Three letters typically follow the symbol where each letter represents two rays and a vertex; the vertex is the middle letter.
For example, ∠ABC represents the angle formed by the rays A and C which intersect at the vertex B. This angle could also be called Angle B.
Angles are measured in comparison to a circle in degrees °. A single degree is this tiny sliver of a circle. It takes 360 slivers, or 360 degrees to fill in an entire circle.
To measure an angle in the offline world, you can use this handy protractor. But you won’t have the luxury of using that little tool on most tests; instead, you have to be able to calculate them using math and remembering some common angle types.
There are five basic types of angles:
It’s helpful to know these angles so well that you don’t have to think about what each one means.
An Acute angle measures less than 90 degrees.
A Right angle measures exactly 90 degrees.
An Obtuse angle is bigger than a right angle but less than 180 degrees.
Because, a 180 degree angle is a Straight angle, aka a line.
And a Reflex angle is more than 180 degrees but less than 360 degrees...because a full 360 degrees is just a circle.
Angles can be either on the inside of a shape, which are called “interior angles” or they can be on the outside of a shape, which are called “exterior angles.”
To measure an exterior angle, you draw an imaginary line from the base of the shape outwards like so. The exterior angle is then formed at the intersection of the shape and your imaginary line.
There are four basic types of interior angle pairings:
Two angles are adjacent when they have a common side and a common vertex and do not overlap.
Vertical angles are formed by two intersecting lines with the opposing angles being equal to each other.
Two angles are complementary when they add up to exactly 90 degrees.
[complementary angle by itself]
And finally supplementary angles add up to exactly 180 degrees.
Note that complementary and supplementary angles do not have to share a common vertex.
On standardized tests, you’re especially likely to get asked about complementary and supplementary angles, so here’s a simple pneumonic to help keep them straight:
Now a quick note note about spelling--complementary is spelled with an “e” and not an “i.” When spelled with an “e,” complementary means to “add to or enhance something.” When spelled with an i, “complimentary” means that something is provided for free.
And you don’t get good at math for free. You have to pay for your skills through hard work and practice!