Angles and their Measure

This section begins our study of Trigonometry and to get started, we recall some basic definitions 
From Geometry. A ray is usually described as a `half-line' and can be thought of as a line segment
in which one of the two endpoints is pushed o_ in_nitely distant from the other, as pictured below.
The point from which the ray originates is called the initial point of the ray.

When two rays share a common initial point they form an angle and the common initial point is called the vertex of the angle. Two examples of what are commonly thought of as angles are

The measure of an angle is a number which indicates the amount of rotation that separates the rays of the angle. There is one immediate problem with this, as pictured below.

Which amount of rotation are we attempting to quantify? What we have just discovered is that

we have at least two angles described by this diagram.1 Clearly these two angles have different

measures because one appears to represent a larger rotation than the other, so we must label them

differently. In this book, we use lower case Greek letters such as α (alpha), β (beta),  γ (gamma) and  θ (theta) to label angles. So, for instance, we have