Sharp square. Types of angles

Let's start by defining what an angle is. Firstly, it is Secondly, it is formed by two rays, which are called the sides of the angle. Thirdly, the latter emerge from one point, which is called the vertex of the angle. Based on these characteristics, we can make a definition: angle - geometric figure, which 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 according to their magnitude.

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

It looks like this:

Its degree measure is always 90 o, in other words, a right angle is an angle of 90 degrees. Only such quadrilaterals as square and rectangle have them.

Blunt

It looks like this:

The degree measure is always more than 90 o, but less than 180 o. It can be found in quadrilaterals such as a rhombus, an arbitrary parallelogram, and in polygons.

Spicy

It looks like this:

The degree measure of an acute angle is always less than 90°. It is found in all quadrilaterals except the square and any parallelogram.

Expanded

The unfolded angle looks like this:

It does not occur in polygons, but is no less important than all the others. A straight angle is a geometric figure whose degree measure is always 180º. You can build on it by drawing one or more rays from its top in any direction.

There are several other minor types of angles. They are not studied in schools, but it is necessary to at least know about their existence. There are only five secondary types of angles:

1. Zero

It looks like this:

The name of the angle itself already indicates its size. Its internal area is 0°, and the sides lie on top of each other as shown in the figure.

2. Oblique

An oblique angle can be a straight angle, an obtuse angle, an acute angle, or a straight angle. Its main condition is that it should not be equal to 0 o, 90 o, 180 o, 270 o.

3. Convex

Convex angles are zero, straight, obtuse, acute and straight angles. As you already understood, the degree measure of a convex angle is from 0° to 180°.

4. Non-convex

Angles with degree measures from 181° to 359° inclusive are non-convex.

5. Full

A complete angle is 360 degrees.

These are all types of angles according to their magnitude. Now let's look at their types according to 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 o.

2. Adjacent

Adjacent angles are formed if a ray is passed through the unfolded angle, or rather through its vertex, in any direction. Their sum is 180 o.

3. Vertical

Vertical angles are formed when two straight 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

A central angle is an angle with its vertex at the center of the circle. Its degree measure is equal to the degree measure of the smaller arc subtended by the sides.

2. Inscribed

An inscribed angle is an angle whose vertex lies on a circle and whose sides intersect it. Its degree measure is equal to half the arc on which it rests.

That's it for the angles. Now you know that in addition to the most famous ones - acute, obtuse, straight and deployed - there are many other types of them in geometry.

Each angle, depending on its size, has its own name:

Angle type	Size in degrees	Example
Spicy	Less than 90°
Straight	Equal to 90°. In a drawing, a right angle is usually denoted by a symbol drawn from one side of the angle to the other.
Blunt	More than 90° but less than 180°
Expanded	Equal to 180° A straight angle is equal to the sum of two right angles, and a right angle is half of a straight angle.
Convex	More than 180° but less than 360°
Full	Equal to 360°

The two angles are called adjacent, if they have one side in common, and the other two sides form a straight line:

Angles MOP And PON adjacent, since the beam OP- the common side, and the other two sides - OM And ON make up a straight line.

The common side of adjacent angles is called oblique to straight, on which the other two sides lie, only in the case when adjacent angles are not equal to each other. If adjacent angles are equal, then their common side will be perpendicular.

The sum of adjacent angles is 180°.

The two angles are called vertical, if the sides of one angle complement the sides of the other angle to straight lines:

Angles 1 and 3, as well as angles 2 and 4, are vertical.

Vertical angles are equal.

Let us prove that the vertical angles are equal:

The sum of ∠1 and ∠2 is a straight angle. And the sum of ∠3 and ∠2 is a straight angle. So these two amounts are equal:

∠1 + ∠2 = ∠3 + ∠2.

In this equality, there is an identical term on the left and right - ∠2. Equality will not be violated if this term on the left and right is omitted. Then we get it.

An acute angle is an angle whose degree measure is less than 90 degrees. A right angle is an angle whose degree measure is 90 degrees. An obtuse angle is an angle whose degree measure is greater than 90 degrees. You can determine each angle using a protractor or ruler.

Acute angle - from zero to 90 degrees (not inclusive).

They look like this

A right angle is 90 degrees, its sides are perpendicular to each other.



There are also obtuse angles - from 90 degrees to 180, this is what they look like:



What angle is in front of you, in general, can be determined by eye, but if you need precise degrees, you need to use a protractor.

It’s simple, take a corner, or a ruler or a protractor, you can do it all together. With a protractor everything is simple, move the appropriate marks, that is, 90% is a right angle; what is greater than 90% -91.99,120,170 is called an obtuse angle; in turn, what is less than 90% - 89, 75, 40.15 is called an acute angle. It's almost impossible to make a mistake.

The angle formed by the intersection of two perpendicular lines is called a right angle. Also, a right angle can arise when dividing a circle into even four parts (1/4 of a circle).

A right angle is 90 degrees.

When the sides of an angle coincide, such an angle is called zero

Zero angle is 0 degrees.

All angles whose degrees are greater than zero and less than right angles are called acute.

An acute angle is greater than 0 degrees and less than 90 degrees.

If the sides of an angle lie in opposite directions and form a straight line, such an angle is called a reverse angle and is equal to 180 degrees.

Angles whose values ​​in degrees are greater than a right angle and less than a straight angle are called obtuse.

An obtuse angle is greater than 90 degrees and less than 180 degrees.



They all have one thing in common:

acute, right and obtuse angles - they are all convex.

An acute angle is one whose value is less than 90 degrees.

Right angle with a 90 degree opening.

An obtuse angle is an angle whose magnitude is greater than 90 degrees but less than 180 degrees.

The right angle is immediately visible to the eye.

Everything is quite simple. Let's make an analogy with an ordinary watch. If one of the hands is set so that it points to twelve o'clock, and the other so that it points to three, then they form a right angle of ninety degrees. If you start moving the hand pointing to three o’clock in the opposite direction (at the two o’clock mark on the dial), then it will form, together with the second hand, sharp angles (less than 90 degrees). When the hands point to one point, they form a zero angle of zero degrees. And if you return the second hand to the original (three o’clock mark) and start moving it forward on the dial, then up to the six o’clock mark it, together with the first, will form obtuse angles ( more than 90 degrees). When the arrows point, one at 12 and the other at 6, this will be the so-called rotated angle of 180 degrees.

In this question you need to start from a right angle:

1.A right angle is 90 degrees



2.Everything angles that are less than a right angle, that is, less than 90 degrees, are considered acute.

For example, angles 89 degrees, 60 degrees, 30 degrees.



3.Everything angles that are greater than a right angle, that is, more than 90 degrees, are considered obtuse.

For example, 91 degrees, 120 degrees, 179 degrees are obtuse angles



It is also necessary to take into account that An angle equal to 180 degrees is called an angle.



This is 7th grade geometry. Perhaps they even take place earlier in school, I don’t remember exactly. A protractor is used to measure the angle. So, a right angle is 90 degrees, sharp corner is always less than 90 degrees (even by 1 degree), and an obtuse angle is always more than 90 degrees.

An acute angle is an angle less than 90.

An obtuse angle is an angle greater than 90 but less than 180.

A right angle is a 90 degree angle.

There is also a straight angle, that is, an angle in the range between 180 and 360.

If the angle is greater than 360, then to find out what angle, you should subtract 360 from the value of this angle and see what remains. If it is still more, then repeat this operation the required number of times.

Angle 0, as well as 180 on one side, are used in calculations as an angle, but in fact they are the beginning of a segment or line, and not an angle.

If you take triangles, then their angles should be in the range between 0 and 180, since at such angles of the triangle (0 and 180) it will no longer be a triangle, but a segment, and with larger angles the triangle will not work.

A right angle is a 90 degree angle found in quadrilaterals such as squares and rectangles.

An obtuse angle is an angle whose degree measure is greater than 90 degrees but less than 180; it is found in rhombuses, polygons, and arbitrary parallelograms.

An acute angle is an angle up to 90 degrees; for example, it does not exist in a square.