To talk about consecutive angles it is important to also first talk about the definition of angle. An angle is the portion of the plane that is between two rays which have a common origin known as the vertex . It can also be said that the angle is the opening formed by two sides that start from that common point, or are centered on the rotation that the plane gives with respect to its origin . When we talk about consecutive angles we refer to an angle relationship that implies the parameters conformants, these parameters are the coplanar lines or rays and the vertex where these lines meet.
What are consecutive angles?
Two angles can be consecutive when one angle is successive to the other, which means that the two angles share the same vertex and one of their rays . When a ray forms two angles on one side and the other , we are faced with two consecutive angles.
- Consecutive interior angles
- How they differ from adjacent angles
- Examples of consecutive angles
We say that two angles that are within the same plane are consecutive when they have only one side in common . According to the extension, given several angles in a certain order , they will then be consecutive when each of them is consecutive with the next.
The word consecutive when we refer to angles means that the angles share at the same time the same vertex as well as one of the sides , which can be the line or ray , in other words they are one next to the other delimited by one of the lines that make them up and, if there are more than two angles , they can continue to be consecutive if the one that follows shares the side of the last one always with the same vertex .
The main characteristics of the consecutive angles are the following:
- Consecutive angles are those that have or share the same vertex.
- They have only one side in common.
- Several angles can become consecutive when each of them shares a side with the angle that follows it.
- The sum that results from the consecutive angles is equivalent to the angle comprised by the infrequent sides of the angles.
- For two angles to be added they must necessarily be consecutive.
- These angles are in the same way placed side by side.
Consecutive interior angles
Consecutive angles are also known with the name of adjacent angles , and the angles are having a side in common and the same vertex . These angles then share a side and a vertex and are located side by side. When the angles are ordered in a certain way, they are said to be consecutive if each angle is successive with the other. When the angles meet consecutively and are interior, it is when two lines are crossed by another transversal call but within both lines.
The sum of the consecutive angles will then be equal to the angle that has been formed by what are the uncommon sides of the angles. When two lines are cut by means of a transversal , the pair of angles on one side of the transversal and within the two lines are called the consecutive interior angles .
The Consecutive Interior Angles Theorem tells us that if two parallel lines are cut by a transversal , then the pairs of consecutive interior angles formed are supplementary.
How they differ from adjacent angles
Consecutive angles have a vertex and a side in common, and these angles are followed one after the other. The adjacent angles are the angles that are found consecutively and that have non-common sides within the same line; are any pair of angles that are in a row but when their degrees are added, a total of 180 ° is obtained.
Examples of consecutive angles
Some examples of consecutive angles are as follows:
- Right angles : Right angles measure 90º and are the result of the perpendicular crossing of two rays.
- Obtuse angles : the obtuse angles are those that measure more than 90º.
- Convex angles : Convex angles are those that measure less than 180º.
- Concave angles : Concave angles are those that measure more than 180º and less than 360º.
- Supplementary angles: Supplementary angles are those that adding the two together give a straight angle.
- Adjacent angles : they have a side and a vertex in common and the other on the same line.
- Central angles in a circle : one whose vertex is located in the center of the circle.