Angle

How Many Degrees in ______ ?

How Many Degrees in a Line

There are 180 Degrees in a Line. This means that if there are two angles across a line, then the sum of those two angles will be 180 degrees. These are known as supplementary angles.

How Many Degrees in Common Shapes

There are a number of common shapes that it is useful to know the number of degrees within.

• Triangle: 180 degrees
• Square: 360 degrees
• Circle: 360 degrees (sometimes also expressed as 2π radians)

How Many Degrees in Any Shape

While normally the common shapes listed above are all that students need to know. Occasionally there are weird shapes in angle problems, and knowing the number of degrees within those shapes may be crucial for answering that question.

Thankfully, there is a simple equation for knowing the number of degrees in any polygon. 

Number of Degrees in a Polygon = 180 (# of sides of the polygon−2)

For example, this is why a triangle has 180 degrees:180 (3−1) = 180  • 1 = 180

Vertical/Opposite Angles

Vertical Angles are angles opposite each other at the intersection of two different lines. The lines can have any slope (they do not have to hit at a right angle or anything special). As long as they are straight lines, opposite/vertical angles will be congruent (have the same measure).

In the illustration below, angle a = angle b

Angles at Intersections with Parallel Lines

When a line intersects a pair of parallel lines, there are a number of set relationships between the angles created by those lines. These are useful to know, because they can be massive time savers. You can save a full minute on an angle question just by going beyond just the supplementary angles rule (which can be tedious to work out with many lines or many shapes).

Depending on which pair of angles are being compared, the angles will either be congruent (equal) or supplementary (adding to 180 degrees), as follows: