# Angles – The Most Crucial Concept of the Subject Mathematics One of the crucial parts of mathematics is geometry. Angles are the most common topic of geometry. In our daily life, we come across a lot of objects in our surroundings. When one will notice it, one will find that all the objects in our world are inclined at some angle with respect to any point or line. An angle is mostly measured in degrees or radians. The majority of shapes have a set angle, such as all three angles of an equilateral triangle being 60 degrees, and all sides of a rectangle and square being 90 degrees. When the angle between two lines is zero degrees, they are said to be parallel, and when the angle between the two lines is ninety degrees, they are said to be perpendicular. As previously said, there are numerous classifications of angles; however, we will focus on corresponding angles. They are categorized into two types. One is formed by parallel lines and a transversal, whereas the other one is formed by two lines that are not parallel and a transversal. Let us first discuss corresponding angles formed due to parallel lines and a transversal.

For understanding corresponding angles due to parallel lines and a transversal, it is necessary to know about parallel lines. One of the major conditions of parallel lines is that they never meet each other at any point. Two lines are said to be parallel lines when the angle between them is equal to zero degrees. The distance between two parallel lines is always constant and it cannot be zero. There are a lot of examples of parallel lines that we observe in our daily life. Railway tracks can be considered as an example for parallel lines. Now let us move our discussion to corresponding angles.

Corresponding angles (parallel lines and transversal): These angles are formed when two parallel lines are cut by the transversal. One can define them as when a third line intersects the two lines which are parallel to each other. The angles that are formed occupy the same relative position at all the intersected points. These angles are termed corresponding angles. Suppose there is a line that crosses both parallel lines. Now at the point where the transverse intersects both the parallel lines, there are a total of four angles formed. So, there will be a total of four pairs of corresponding angles formed with each parallel line. Now, one should also know that the corresponding angles that are formed by the parallel lines are always equal. When the transverse cuts the two parallel lines, not only corresponding angles are formed but few other angles are also formed like alternate interior and exterior angles.

Corresponding angles (non-parallel lines and transversal): In this case, when the transverse cuts the other two lines, then corresponding angles are formed. But in this case, there is no relation between the corresponding angles formed or we can say that the corresponding angles formed are not equal in this case as it was in parallel lines. Students need to have these concepts clear in their minds so that they can tackle tough mathematical problems more accurately and easily.

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