Question

In the figure below, point H is the incenter of DEF, and m DHF=130. What is the measure of DEF?

Answer 1

The answer would be 80?

That is correct!

Explanation:

Once Im done with the question Ill come back and make sure its correct!

Answer 2

The measure of angle DEF is ∠DEF=80°

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°