Answer:
The measure of angle DEF is ∠DEF=80°
Step-by-step explanation:
we know that
The incenter is constructed by taking the intersection of the angle bisectors of the three vertices of the triangle
The triangle DEF is an isosceles triangle
∠EDF=∠EFD
so
In the triangle DHF
∠HDF=∠HFD
∠HDF+∠DHF+∠HFD=180°
substitute the value
2∠HDF+130°=180°
∠HDF=25°
therefore
∠EDF=2*25°=50°
In the triangle DEF
∠EDF+∠DEF+∠EFD=180°
∠EDF=∠EFD=50°
substitute
50°+∠DEF+50°=180°
∠DEF=80°
