Consecutive angle

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A consecutive angle is one that shares a side and a vertex in common with another.

That is, two angles are consecutive if one is next to the other, both having in common some of the segments, rays or lines that form them. Thus, they are born from the same point.

In the image above, for example, α and β are consecutive angles.

Consecutive angles are one of the categories of angles based on their position relative to another angle.

We must remember that an angle is an arc that is formed by the crossing of two lines, rays or segments.

Types of angles

Difference between consecutive and adjacent angle

It should be noted that a consecutive angle is not the same as an adjacent one. In the latter case, an additional condition must be fulfilled → The angles must be supplementary. In other words, two angles are adjacent if they are consecutive and, at the same time, add or form a straight angle of 180º (sexagesimal degrees) or π radians.

In sum, an adjacent angle is a particular type of consecutive angle. Thus, in the image shown above, we observe two angles that are consecutive, but not adjacent, since they add up to more than 180º.

Examples of consecutive angles

Let's look at some examples of consecutive angles:

  • Let's imagine we have a quadrilateral and we draw its diagonals. Then, each of its interior angles will be divided into two 45º angles that are consecutive.
  • For a less abstract example, suppose we have a stake driven into the ground. The angle that the ground makes with the right side of the stake is consecutive to the angle that the ground makes with the left side of the stake.

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