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.