Triangle def is isosceles, where . angle fde is bisected by segment dg, creating angle gde with a measure of 29°.

⇒ ∠DFE = 64°    

Step-by-step explanation:

Given that : ΔDEF is an isosceles triangle. ∠FDE is bisected by segment DG

To find : m∠DFE

Solution :

∠FDE is bisected by segment DG creating ∠GDE = 29°

⇒ m∠FDE = 2 × ∠GDE

⇒ m∠FDE = 2 × 29°

⇒ m∠FDE = 58°

Since, ΔDEF is an isosceles triangle

⇒ FD = FE

⇒ ∠FDE = ∠FED (Angles opposite to equal sides are equal)

⇒ ∠FED = 58°

Now, Using angles sum property of a triangle

∠FDE + ∠FED + ∠DFE = 180°

⇒ 58° + 58° + ∠DFE = 180°

⇒ ∠DFE = 180 - 114

⇒ ∠DFE = 64°