The value of m∠EDF = 51.5° using the isosceles triangle theorem
Using the isosceles triangle theorem which state that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent.
i.e ED = EF
∠EDF = ∠EFD
Where ∠DEF + ∠EFD + ∠EDF = 180°
So, 77° + x + x = 180°
x + x = 180° - 77°
2x = 103°
Divide through by 2
x = 103/2
x = 51.5°
Therefore, m∠EDF = 51.5° using the isosceles triangle theorem