Knowing the etymological origin of the two words that give shape to the term consecutive angles is what we are going to do now. In that case this is what you need to know:
-Angle comes from the Greek word “ankulos”, which meant “crooked”, and which was passed into Latin with the current meaning of angle through “angulus”.
-Consecutive, on the other hand, comes from Latin. It is exactly derived from “consecutivus”, which can be translated as “the one who continues without interruption.” It is formed by the sum of three clearly differentiated elements: the prefix “with”, which can be translated as “together”; the verb form “sequi”, which can be translated as “follow”, and finally the suffix “-tive”. This is used to indicate a passive or active relationship.

A angle It is a figure of geometry that is formed by two rays that share the vertex of origin. Consecutive, for its part, is an adjective that refers to that which immediately follows a thing. The consecutive angles, also called contiguous angles, are angles that have a common side and the same vertex. These angles, therefore, share a side and vertex and are located next to each other.

The sum of the consecutive angles equals the angle formed by what are the non-common sides of the angles.

It should be noted that consecutive angles are also adjacent angles: The definition of adjacent angles refers to a shared side and vertex, but also adds that the other two sides must be opposite rays.

It is exactly determined that the adjacent angles are angles that are both complementary and consecutive.

The conjugated angles, on the other hand, are consecutive angles. The theory indicates that the conjugated angles have their sides and the vertex of origin in common, like the consecutive ones, and add 360º (a perigonal angle).

We can find consecutive angles in certain cases of complementary angles. Recall that the complementary angles add 90º. When these two complementary angles are consecutive, the sides that do not have in common form the right angle in question.

Supplementary angles, whose peculiarity is that they add up to 180º (a straight angle), can also be consecutive angles when their vertex and one of their sides are shared.

It should be considered that each consecutive angle of another can be a acute angle (measures more than and less than 90º), a right angle (90º) or a obtuse angle (more of 90º and less than 180º).

In addition to these types of angles that we are dealing with, there are many others equally important within the field of mathematics such as opposite angles. These are the ones that are characterized because they have a common vertex and the sides of one come to be what is the prolongation of the others.
In the same way, we cannot ignore either that there are cases of convex angles, concave angles and even plain angles that are considered consecutive angles.