Let's start by defining what an angle is. Firstly, he is a geometric figure. Secondly, it is formed by two rays, which are called the sides of the angle. Thirdly, the latter come from one point, which is called the vertex of the angle. Based on these signs, we can make a definition: an angle is a geometric figure that consists of two rays (sides) emerging from one point (vertex).
They are classified by degree value, by location relative to each other and relative to the circle. Let's start with the types of angles in their size.
There are several varieties of them. Let's consider each view in more detail.
There are only four main types of angles - a straight, obtuse, sharp and unfolded angle.
Straight
It looks like this:
Its degree measure is always 90 degrees, in other words, the right angle is the angle of 90 degrees. Only quadrangles such as a square and a rectangle have them.
Stupid
It looks like this:
The degree measure of an obtuse angle is always greater than 90 about , but less than 180 about . It can be found in such quadrangles as a rhombus, an arbitrary parallelogram, in polygons.
Acute
It looks like this:
The degree measure of an acute angle is always less than 90 about . It is found in all quadrangles except a square and an arbitrary parallelogram.
Deployed
The expanded angle has the following form:
It does not occur in polygons, but it is no less important than everyone else. The expanded angle is a geometric figure whose degree measure is always 180º. Adjacent angles can be built on it by drawing one or more rays from any of its vertices in any direction.
There are a few minor kinds of angles. They are not studied in schools, but it is necessary to know at least about their existence. There are only five minor types of angles:
1. Zero
It looks like this:
The very name of the corner already speaks of its size. Its inner region is 0 °, and the sides lie on each other as shown in the figure.
2. Oblique
Oblique can be a straight line, and a blunt, and a sharp, and a developed angle. Its main condition is that it should not be 0 , 90 , 180 , 270 .
3. Convex
Convex are zero, straight, obtuse, sharp and unfolded angles. As you already understood, the degree measure of a convex angle is from 0 about to 180 about .
4. Convex
Angles with degree measure from 181 ° to 359 ° inclusive are non-convex.
5. Full
The full angle is 360 degrees.
These are all types of angles in their size. Now consider their views in terms of their location on the plane relative to each other.
1. Additional
These are two acute angles forming one straight line, i.e. their sum is 90 about .
2. Related
Adjacent angles are formed if a beam is drawn in any direction through the unfolded, more precisely, through its top. Their sum is 180 about .
3. Vertical
Vertical angles are formed at the intersection of two lines. Their degree measures are equal.
Now we turn to the types of angles located relative to the circle. There are only two of them: central and inscribed.
1. Central
The center is the corner with the peak in the center of the circle. Its degree measure is equal to the degree measure of a smaller arc pulled together by the sides.
2. Inscribed
An inscribed angle is an angle whose vertex lies on a circle and whose sides intersect it. His degree measure is equal to half the arc on which he relies.
That's all for the corners. Now you know that in addition to the most famous - sharp, blunt, straight and unfolded - in geometry there are many other types of them.