Corresponding angles are formed when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other. This implies that for these angles to be formed, there must be two parallel lines intersected by a transverse line.
In this article, we are going to look at some examples of corresponding angles and solve them.
In the second diagram, <2 and <6, <3 and <7, <1 and <5, <4 and <8 are corresponding
Corresponding Angles Theorem
If a transversal intersects two parallel lines, then each pair of corresponding angles is equal. Conversely, if a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel.
Examples of Corresponding Angles
(1) Which of the following are corresponding angles?
In the above diagram, there are two parallel lines i.e line 1 || line 2 and a transverse line intersecting the parallel lines.
Therefore, corresponding angles in the figure above are listed below:
<b and <f
<c and <g
<a and <e
<d and <h
(2) In the diagram below, K, m, n are parallel lines. What is the value of the angle marked x?
Looking at the above figure keenly, a = 117 (corresponding angles are equal). Also, b = a = 117 (corresponding).
Then, b + x = 180 (sum of angles on a staright is 180)
x + 117 = 180
x = 180 -117 = 63
So, the angle x is 63