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Alternate angles are defined as pairs of angles that are formed when a transversal intersects two parallel lines, and they are located on opposite sides of the transversal but inside the parallel lines. In the context of this question, the correct pair identifiable as alternate angles are those that lie at different ends of the transversal.
These angles are important in geometry because they are equal in measure when formed by a transversal crossing parallel lines. This property is often used to establish relationships between angles in various geometric proofs or problems.
The other choices do not accurately describe alternate angles. For instance, angles on the same side of a transversal would be classified as corresponding angles, while angles that are opposite each other at the intersection refer to vertically opposite angles. Angles formed inside the parallel lines could refer to alternate interior angles, but to specifically identify alternate angles, the positioning related to the transversal must be emphasized.