What are Alternate Angles in Geometry?

A transversal is a line formed by the intersection of two or more parallel lines. Several pairs of angles are formed when a transversal is made over parallel lines. When a transversal intersects two parallel lines, it creates four interior angles on the inside and four external angles on the outside. These are called alternate angles.

To illustrate the concept, the two parallel lines a transversal xy cuts ab and cd in the illustration below. The external angles are angles ∠1, ∠2, ∠7, and ∠8. The inner angles are angles ∠3, ∠4, ∠5, and ∠6.

Alternate Angles Definition in Geometry

Alternate angles are the angles formed by intersecting lines and a transversal line, refer to a pair of angles that are located on opposite sides of the transversal line and on different lines.

Angles ∠3 and ∠6, ∠4 and ∠5, ∠1 and ∠8, and ∠2 and ∠7 are alternates.

Read More,

• Parallel Lines
• Parallel Lines and Traversal

Types of Alternate Angles

There are two types of alternative angles:

Alternate Interior Angles: Angles on the inside of two parallel lines but on opposite sides of the transversal.

Take note of the specified angles and how each pair of angles is equal to each other.

Alternate Exterior Angles: The pair of angles on the outer edge of two parallel lines but on opposite sides of the transversal.

Take note of the alternate exterior angles and how they are equal to each other.

Alternate Exterior Angles in maths are generated when a transversal connects two or more parallel lines at different locations. Alternate exterior angles are a pair of angles that lie on the opposite sides of a transversal line and on the outer sides of two intersecting lines. When a transversal line intersects two other lines, it creates several pairs of angles, and alternate exterior angles are one of these pairs. You can also check the article on parallel lines and traversal to study it in detail.

The phrase exterior refers to something that is located on the outside. They are placed on opposing sides of the transversal and lie outside the two crossed lines. As a result, the two external angles formed at the opposite ends of the transversal in the outside component are termed a pair of alternative exterior angles and are always equal. When a transversal intersects two parallel lines, we obtain two such pairs of alternate exterior angles.

In this article, you will study what are alternate exterior angles, the alternate exterior angles theorem, and examples of alternate exterior angles.