Answer: measure an angle, we place the vertex at the center of a The vertex of an angle
Explanation:
An angle is the opening that two straight lines form when they meet.
angles
When the straight line FA meets the straight line EA, they form the angle we name as angle FAE. Letter A, which we place in the middle, labels the point where the two lines meet, and is called the vertex of the angle. When there is no confusion as to which point is the vertex, we may speak of "the angle at the point A," or simply "angle A."
The two straight lines that form an angle are called its sides. And the size of the angle does not depend on the lengths of its sides. We can see that in the figure above. For if the point C is in the same straight line as FA, and B is in the same straight line as EA, then angles CAB and FAE are the same angle.
Now, to measure an angle, we place the vertex at the center of a
The vertex of an angle
circle (we call that a central angle), and we measure the length of the arc -- that portion of the circumference -- that the sides intercept. We then determine what relationship that arc has to the entire circumference, which is an agreed-upon number. (In degree measure that number is 360; in radian measure it is 2π.)
The measure of angle A, then, will be length of the arc BC relative to the circumference BCD -- or the length of arc EF relative to the circumference EFG. For in any circles, equal central angles determine a unique ratio of arc to circumference. (See the theorem of Topic 14. It is stated there in terms of the ratio of arc to radius, but the circumference is proportional to the radius: C = 2πr.)
There are two systems for measuring angles. One is the well-known system of degree measure. The other is the strictly mathematical system called radian measure, which we take up in the next Topic.
