In Geometry, there is a special type of angle called alternate angles. Alternate angles are non-adjacent and set angles on the contrary sides of the transversal.
In this write-up, we will talk about alternate exterior angles and their theorem. Before entering into this subject, it is essential to recall the following terms: angles, transversal, and parallel lines.
For that, you need to undergo the previous write-ups on Angles.
What are Alternate Exterior Angles?
Alternate exterior angles are the pair of angles that lie on the outer side of both parallel lines but on either side of the transversal line.
Alternating exterior angle theorem.
An alternate exterior angle specifies that the resulting alternate exterior angles coincide when a transversal reduces two parallel lines.
Concerning the representation over:
∠ A = ∠ d.
∠ b = ∠ c.
Alternate exterior angles are created when at distinct points, the transversal intersects two or more parallel lines. The term exterior points to something that is situated externally. Such angles always lie outside two lines converged by the transversal and are found on other sides of the transversal. Thus, the two exterior angles that form at the alternate ends of the exterior component transversals are the pair of alternate exterior angles and are always equivalent. When a transversal cuts two parallel lines, we obtain two alternate exterior angles. Let us learn more about them.
Alternate Exterior Angles Meaning
Two angles that rest on opposite sides of the transversal and are positioned on two different lines are called alternate exterior angles. These sets of angles are always equal if both provided lines are identical. In the given number listed below, Line AB|| Line CD and also they are intersected by the transversal MN. The alternate exterior angle pairs are ∠ one and ∠ 7, ∠ 2 and ∠ 8. This suggests ∠ 1 = ∠ 7; ∠ 2 = ∠ 8.
Read Also: Vertical Angles – A Brief Overview
We can see that ∠ two get on the right side of the transversal M, two are above the line AB, eight are on the left, and ∠ eight are below the line CD. The same guideline obtains the other angles (∠ 1 and ∠ 7). For that reason, both angles that please these conditions are called alternate exterior angles.
A quick note on Alternate Exterior Angles
Alternate exterior angles are created when a transversal intersects two or more lines. These angles are based on the external side of the transversal on the various sides.
When a transversal intersects any two parallel lines, they produce some pairs of angles with the transversal. Inside angles are available within the parallel lines; however, alternate exterior angles are created outside the parallel lines.