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Triangle DEF is isosceles, where . Angle FDE is bisected by segment DG, creating angle GDE with a measure of 29°.

Triangle DEF is isosceles where Angle FDE is bisected by segment DG creating angle GDE with a measure of 29 class=

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crusherofjerich1
your answer is D. 64. 

Answer:

⇒ ∠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°    

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