Let's start by defining what an angle is. First, it is a geometric figure. Secondly, it is formed by two rays, which are called the sides of the angle. Thirdly, the latter come out of one point, which is called the apex of the corner. 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 degrees, by location relative to each other and relative to the circle. Let's start with the types of angles by their size.
There are several varieties of them. Let's take a closer look at each type.
There are only four main types of angles - straight, obtuse, acute and straight angles.
Straight
He looks like this:
Its degree measure is always 90o, in other words, a right angle is an angle of 90 degrees. Only such quadrilaterals as a square and a rectangle have them.
Stupid
It looks like this:
The degree measure of an obtuse angle is alwaysmore than 90o, but less than 180o. It can occur in such quadrilaterals as a rhombus, an arbitrary parallelogram, in polygons.
Spicy
He looks like this:
The degree measure of an acute angle is always less than 90o. It occurs in all quadrilaterals, except for a square and an arbitrary parallelogram.
Expanded
The expanded corner looks like this:
It does not occur in polygons, but it is no less important than all the others. A straight angle is a geometric figure, the degree measure of which is always 180º. Adjacent angles can be built on it by drawing one or more rays from its vertex in any direction.
There are a few more secondary types of corners. They are not studied in schools, but it is necessary to know at least about their existence. There are only five secondary types of angles:
1. Zero
He looks like this:
The very name of the angle already speaks of its magnitude. Its interior area is 0o and its sides lie on top of each other as shown.
2. Oblique
Slanting can be straight, and obtuse, and acute, and developed angle. Its main condition is that it should not equal 0o, 90o, 180o, 270 o.
3. Convex
Convex are zero, right, obtuse, acute and developed angles. As you already understood, the degree measure of a convex angle is from 0o to 180o.
4. Non-convex
Non-convex are angles with a degree measure from 181o to 359o inclusive.
5. Full
A full angle is a 360 degree measureo.
These are all types of angles according to their size. Now consider their types by location on the plane relative to each other.
1. Additional
These are two acute angles forming one straight line, i.e. their sum is 90o.
2. Related
Adjacent angles are formed if a ray is drawn in any direction through a deployed, or rather, through its vertex. Their sum is 180o.
3. Vertical
Vertical angles are formed when two lines intersect. Their degree measures are equal.
Now let's move on to the types of angles located relative to the circle. There are only two of them: central and inscribed.
1. Central
Central is the corner with the vertex at the center of the circle. Its degree measure is equal to the degree measure of the smaller arc contracted by the sides.
2. Inscribed
An inscribed angle is an angle whose vertex lies on the circle and whose sides intersect it. Its degree measure is equal to half of the arc it rests on.
It's all about the corners. Now you know that in addition to the most famous - sharp, blunt, straight and deployed - there are many other types of them in geometry.
