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Alternate Exterior angles formed by Non-Parallel lines and their Transversal

animation to understand formation of alternate exterior angles formed by non-parallel lines and their transversal

A pair of exterior angles, formed by the intersection of nonparallel lines and their transversal are called alternate exterior angles.

When two nonparallel lines are cut by their transversal, four exterior angles are possibly formed geometrically. Two of them are opposite to each other and other two exterior angles are opposite to each other. Hence, they are called alternate exterior angles.

Alternate Exterior Angles

alternate exterior angles formed by non-parallel lines and their transversal

In this example, four exterior angles $\angle BPX$, $\angle XPA$, $\angle CQY$ and $\angle YQD$ are formed.

The $\angle CQY$ and the $\angle BPX$ are opposite to each other and they are called alternate exterior angles. Similarly, $\angle XPA$ and $\angle YQD$ are opposite to each other. So, they are also called as alternate exterior angles.

Remember, alternate exterior angles are not equal because of the non-parallelism of the straight lines.

$(1) \,\,\,\,\,\,$ $\angle BPX \ne \angle CQY$

$(2) \,\,\,\,\,\,$ $\angle XPA \ne \angle YQD$



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