## Frequently Asked Questions

#### 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.