Each angle has its own degree value.
This is known to schoolchildren since the early years.
But soon the curriculum introduces the notion of a degree arc measure, and new tasks require the ability to correctly calculate it.
An arc is a part of a circle enclosed betweenTwo points lying on this circle. Any arc can be expressed in terms of numerical values. Its main characteristic along with the long is the value of the degree measure.
The measure of the arc of a circle, like the angle,Measured in the degrees themselves, of which 360, or in minutes, which in turn are divided into 60 seconds. On the letter, the arc is indicated by an icon that resembles the lower part of the circle and with letters: two capital letters (AB) or one lowercase (a).
But when one arc is singled out on a circleInvoluntarily formed another. Therefore, in order to unambiguously understand which arc is involved, mark on the selected arc one more point, for example, C. Then the notation becomes ABC.
A segment that is formed by two points bounding an arc is a chord.
The degree of the arc can be found in terms ofInscribed angle, which, having a point of the vertex on the very circumference, rests on this arc. Such an angle is called in mathematics inscribed, and its degree measure is equal to half the arc on which it rests.
Also in the circle there is a central angle. It also rests on the desired arc, and its apex is no longer on a circle, but in the center. And its numerical value is no longer half the degree of the arc, but its whole value.
Having understood how the arc is calculated through theIts angle, we can apply this law in the opposite direction and deduce the rule that the inscribed angle that rests on the diameter is straight. Since the diameter divides the circle into two equal parts, it means that any of the arcs has a value of 180 degrees. Therefore, the inscribed angle is 90 degrees.
Also, based on the method for finding the degree value of the arc, the rule is that angles that are based on one arc have an equal value.
The value of a degree arc measure is often used to calculate the length of a circle or the arc itself. To do this, use the formula L =? * R *? / 180.