We need to find the measure of ∠ 16. Let's find that angle on the given diagram.
We can see that ∠ 14 and ∠ 16 are formed by two parallel lines and the transversal. They both lie on the same side of the transversal and on the same left side of the parallel lines. According to the definition, these are called corresponding angles. Therefore, to find the measure of ∠ 16, 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 ∠ 14 and ∠ 16 are congruent, so their measures are the same. From the previous exercise we know that m∠ 14=57. Therefore, the measure of ∠ 16 is also 57.
