We know that the measure of angle ∠ 11 is 62 and the measure of ∠14 is 38. Consider where these angles are located on the diagram.
In order to find the measure of angle ∠ 3, we need to find its relationship with one of these angles.
We see that ∠ 3 and ∠ 11 are formed by the parallel lines and the transversal. They lie on opposite sides of the transversal and on different sides of the parallel lines. According to the definition, these are alternate exterior angles. Therefore, to find the measure of ∠ 3, we can use Alternate Exterior Angles Theorem.
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
By the theorem, we conclude that ∠ 11 and ∠ 3 are congruent, so their measures are the same. Therefore, the measure of ∠ 3 is also 62.
