You can find angles when two straight lines intersect, two rays emanate from the same point or in geometric figures. Different types of tendencies can arise there, which are described differently.
There are angles in almost every branch of mathematics. Therefore, they accompany you until you graduate from school. This article takes a closer look at the different types of angles and how to recognize them.
The angle
Before you get to know the different types of angles, the parameters that make up an angle are repeated.
If two lines g and h intersect at a point, this point is called the point of intersection S of lines g and h. The two straight lines span the angle α at their point of intersection. This angle α can be either in degree or in radians be specified.
Figure 1: Angle parameters
This illustration is an example of one single angle. When two or three straight lines intersect, angles are formed, each of which has a specific relationship to one another. If it is about the relationship of two angles, one speaks of angle pairs.
Overview of all angle types with names and degrees
Due to the different inclination of the rays or straight lines, a number of different types of angles arise. These are classified into one of them based on their degree of tilt seven categories assigned.
detect zero angle
As the name suggests, the zero angle has one angle from 0 degrees. In principle, you can’t see any angle here, there the two legs lie directly on top of each other.
For zero angle is applicable:
Figure 2: Zero Angle
In memory of: Legs are two straight lines that together form an angle.
Recognize acute angles
The acute angle is a Angles between 0 and 90 degrees and is referred to as pointed because of the slope and appearance. The angle is greater than 0 degrees. So there is not just a line, but an angle. On the other hand, the angle is also less than 90 degrees, i.e. less than a quarter of the circle.
Figure 3: acute angle
Right angle
A right angle is one angle of exactly 90 degrees. Usually you can do it with a point inside the angle mark (see figure below). At the right angle they are Thighs exactly perpendicular to each other. You can imagine that this is exactly one quarter of a circle is.
For right angle is applicable:
Figure 4: right angle
obtuse angle
Obtuse angles are angles whose Tilt between 90 and 180 degrees lies. So there is more than a quarter turn but less than a half turn.
For obtuse angles is applicable:
Figure 5: obtuse angle
straight angle
When the angle is straight Tilt at exactly 180 degrees. As a result, the legs point exactly in the opposite direction and thus form a straight line. The angle is then just as large as that half of a circle.
For straight angles is applicable:
Figure 6: straight angle
Obtuse angle
At a Tilt between 180 and 360 degrees is spoken of an obtuse angle. That’s more than half a turn, but less than a full turn.
For reflex angles is applicable:
Figure 7: reflex angle
Determine full angle
A full angle is an angle at which a more complete Circle was pulled, which is why Angle 360 degrees Has. Even with a full angle, the legs are on top of each other and point in the same direction, just like with a zero angle. Therefore it is always a matter of interpretation whether it is a full or zero angle. A full revolution corresponds to a full angle.
For full angle is applicable:
Figure 8: Full angle
If you want to measure an angle, you can use a set square. Sometimes, however, the sides of the square are not long enough to take an accurate measurement on the protractor.
If that’s the case, just use your pen to extend the respective legs. Since the slope between the straights or rays doesn’t change, the angle stays the same and you can easily read its size because of the longer legs.
You can find out more about this in the article «Measuring angles».
Types of angles in radians
Angles can be measured not only in degrees (°), but also in radians be specified.
That radians is the length of the arc b on the unit circle.
The unit circle is a circle with radius 1.
Figure 9: Unit circle
The full rotation, i.e. 360°, corresponds to on the unit circle.
180° in radians is half, so just one, and 90° is a quarter, so . You can always convert it like this or you use the formula.
The formula for converting angles from degrees to radians reads:
The formula for converting angles from radians to degrees reads:
It may help you in many tasks if you know that you can specify angles in other ways and also convert the units. An angle is often specified in radians and it is assumed that you know what that is.
Ratios of angles in intersecting lines
When straight lines intersect, there are always at least 4 angles. These angles then have different relationships to each other. So it is divided into single angles and pairs of angles distinguished.
determine the vertex angle
If intersect two straight lines, four different angles are formed at the point of intersection between the lines. here are the opposite angles are always the same size. You will as vertex angle designated.
In the figure, the pairs of vertical angles are marked in the same color:
Figure 10: Apex angle
secondary angle
If intersect two straight linesthen become two adjacent angles always as secondary angle designated. the Sum of an angle and one of its secondary angleor the sum of two secondary angles, always results in 180 degrees (i.e. a straight angle).
For secondary angle is applicable:
An example of secondary angles is each marked in the same color:
Figure 11: Secondary angle
Recognize step angle
if two parallel straight lines now intersected by another straight line are made, ratios between the angles of the various points of intersection can be identified. Step angles are formed, among other things.
step angle are the angles that are offset from each other on the same side of the points of intersection. They are always the same size.
You can also imagine this as if the straight lines with the angles would form the letter F. The step angles are then in each case at the crossing points of the lines. Because of this, step angles are sometimes also called «F Angle» designated.
In the figure, the step angles are marked in the same color.
Figure 13: Step angle
recognize changing angles
Alternating angles arise, like step angles, when e.gtwo parallel lines are intersected by a third line.
A alternating angle is basically like one vertex angle, only at the other intersection. Alternating angles are equal. In a case like this, with three lines involved, there are four pairs of alternating angles.
You can also imagine this as if the straight lines together form a Z. the Alternating angles then lie exactly in the niches of the Z. That’s why sometimes they will «Z angle» called.
Generally applies to alternating angle:
- They lie on different sides of the line of intersection g.
- They lie on different sides of the parallel intersecting line h and f.
Mathematically, this can be formulated as follows:
In the figure, the angles that are marked in the same color each form a pair of alternating angles. There are four different pairs here.
Figure 14: Alternating angle
Types of angles – the most important
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It is broken down into single angles and pairs of angles distinguished.
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single angle:
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Zero angle (α = 0°)
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acute angles (0° < α < 90°)
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right angles (α = 90°)
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obtuse angles (90° < α < 180°)
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straight angles (α = 180°)
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reflex angles (180° < α < 360°)
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full angle (α = 360°)
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Pairs of angles for two intersecting straight lines:
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Pairs of angles in two parallel lines intersected by a third line: