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 ∠ 6, we need to find its relationship with one of these angles.
We see that ∠ 6 and ∠ 14 are formed by the parallel lines and the transversal. They both lie on the same side of the transversal and on the same right side of the parallel lines. According to the definition, these are called corresponding angles. Therefore, to find the measure of ∠ 6, we can use Corresponding Angles Postulate.
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
By the postulate, we conclude that ∠ 6 and ∠ 14 are congruent, so their measures are the same. Therefore, the measure of ∠ 6 is also 38.
