Question

triangle def is isosceles, where $overline{df}congoverline{fe}$. angle fde is bisected by segment dg, creating angle gde with a measure of 29°. what is the measure of angle dfe? 29° 32° 58° 64°

Explanation:

Step1: Find angle FDE

Since DG bisects angle FDE and angle GDE = 29°, then angle FDE=2×29° = 58°.

Step2: Use isosceles - triangle property

In isosceles triangle DEF where DF = FE, angle FDE = angle FED = 58°.

Step3: Calculate angle DFE

Using the angle - sum property of a triangle (the sum of interior angles of a triangle is 180°), let angle DFE be x. Then x+58° + 58°=180°. Solving for x: x = 180°-(58° + 58°)=64°.

Answer:

64°