Measuring Angles

Links and useful resources

We're working with some geometry now, so we need to know what the names of things are. Here's a list:

A point is a speck, or a thing that has no properties other than a position
A line extends infinitely in both directions
A ray starts at a point called the origin and extends to infinity in only one direction
A segment is a straight path between two points
An angle is formed by two rays that share their origin
The rays of an angle are called its sides
The vertex of the angle is the origin of both of its rays
Angles are measured in two main ways: degrees and radians.
A degree is $\frac{1}{360}$ of the way around a circle, or $\frac{1}{180}$ of the way around a semicircle
A radian is the ratio of the arc length of a piece of a circle to the radius of that circle. There are $π$ radians in a semicircle, and $2 π$ radians in a full circle.

Angles measure relative direction of things. Here is a list of things you'll need to know:

Angles are adjacent if they share a side and vertex.
Adjacent angles can be added up just like numbers to get the total angle spanned by both.
Adjacent angles that add up to $90 °$ are called complementary angles
Adjacent angles that add up to $180 °$ are called supplementary angles
A line with a point somewhere on it is a $180 °$ angle, and is also called a straight angle
Adjacent angles that go all the way around and back to where they started add up to $360 °$

Using a protractor is easy, but there are some common mistakes. Here's what you have to do:

The common mistakes are:

thinking the center mark of the protractor is on the bottom edge. The center mark is usually NOT on the bottom edge of the protractor! If you put your vertex there, you'll get the wrong answer
Reading the wrong number for the angle. The protractor has angles that you can read in either direction. In order to do it right, read the angle from the arc of numbers that has a zero on the other side of your angle. When you started, you aligned the baseline of the protractor with one arm of the angle. You should read the angle from the number track that has a zero there.
Not aligning the baseline correctly. Make sure the baseline of the protractor is exactly above one side of the angle!