Question

What is angle DFE? 119 42 19 78

Answer 1

∠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°