Alternate exterior angles

When a transversal intersects two lines, it forms two pairs of alternate exterior angles. The alternate exterior angles are the opposing pair of exterior angles formed by the transversal and the two lines.

In the diagram below, transversal l intersects lines m and n. ∠1 and ∠4 is one pair of alternate exterior angles, and the other pair is ∠2 and ∠3.

If two lines in a plane are cut by a transversal so that any pair of alternate exterior angles is congruent, the lines are parallel. Conversely, if two lines are parallel, any pair of alternate exterior angles is congruent.

Lines m and n above are cut by transversal l where ∠1≅∠4 so, m//n (// is the symbol for parallel).


Find the measures of angles 1, 2, and 4 below given that lines m and n are parallel.

Since lines m and n are parallel, ∠2=60°. Since ∠1 and ∠2 form a straight angle, ∠1=180°-60°=120°. Similarly, since the angle measuring 60° adjacent to ∠4 form a straight angle, ∠4=120°.