 #### What are the basic properties of angles?

Once 360 degrees has been defined as the angle through which to turn for one complete rotation, we quickly establish other useful facts. A half turn, or the amount of turn about a single point on a straight line is 180 degrees, and a quarter turn, or a right angle, is represented by 90 degrees.

This leads us to our first important result. Consider a pair of intersecting lines. It is clear that a + b = 180 (angles on a straight line) and b + c = 180. Therefore a + b = b + c and so a = c. That is, opposite angles are equal; this result is called the X angle property.

Let us now consider a line intersecting a pair of parallel lines. As the line intersects the parallel lines in the same direction, it is self-evident that a = b. This is called the F angle property.

Consider the following diagram. By the F angle property, a = c and by the X angle property, a = b, hence we establish the Z angle property, which states that b = c.

We are able to use the Z angle property to determine the sum of angles in a triangle. It should be clear that a + b + c = 180. That is, the sum of interior angles in a planar triangle is 180 degrees.