Answer:
∠DFE=119°
Explanation:
step 1
Find the measure of angle BFD
we know that
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
so
∠BFD=(1/2)[arc BD+arc CE]
substitute the given values
∠BFD=(1/2)[38°+84°]
∠BFD=61°
step 2
Find the measure of angle DFE
we know that
∠BFD+∠DFE=180° -----> linear pair (supplementary angles)
substitute
61°+∠DFE=180°
∠DFE=180°-61°=119°