To find the measure of ∠ 2, we can notice that FD is a transversal cutting lines FC and ED.
Angles ∠ 2=∠ DFC and ∠ EDF are alternate interior angles.
The markers on segments FC and ED indicate that these segments are parallel. Thus, according to the Alternate Interior Angles Theorem, ∠ 2 and ∠ EDF are congruent, so their measures are the same. Since m∠ EDF=39 is given on the figure, this gives the measure of ∠ 2.
m∠ 2=39^(∘)
Finding m∠ 3=m∠ CDF
Let's put the measure of ∠ 2=∠ DFC we just found on the diagram and focus on the right triangle △ CDF.
As in finding m∠ 1, we can again use that acute angles of a right triangle are complementary to find m∠ 3.
