But What IS an Angle?

You probably know an angle when you see one. In fact, the word “angle” derives from a Greek word for “elbow.” So an angle usually has a “bend” to it. In geometry we need to be a little more precise than that. An angle actually consists of two rays with a common vertex. There are no restrictions other than that. A ray is like a “half line” that it goes on forever, but in only one direction, and the point where it starts is called its “vertex.”

The rays that make up an angle are called its “sides” and it is important to realize that they have infinite length. Since we can’t draw things of infinite length, we are forced to draw the sides as segments. But the length of those segments is not an indication of how “large” an angle is. For example, both of these angles are the same size even though the angle on the left looks smaller because its sides are drawn smaller:

The “size” of an angle can be measured in degrees using a protractor. This is equivalent to drawing a circle centered at its vertex, dividing the circle into 360 equally-spaced marks and then counting the number of marks between the sides of the angle. If the sides are drawn too short to fit a protractor, you have to extend them. For example to measure the angle above (both drawings represent the same angle) you would place its vertex at the origin of the protractor and one side along the horizontal, like this:

This angle measures 30 degrees.

Angles have an “interior” which is the region between the sides. More precisely, the interior of an angle is the region containing all segments that can be drawn connecting the two sides:

toc | return to top | previous page | next page