Question

triangle def is isosceles, where df = fe. angle fde is bisected by segment dg, creating angle gde with a measure of 29°. what is the measure of angle dfe? 29° 37° 58° 64°

Explanation:

Step1: Understand the property of isosceles triangle

In an isosceles triangle \(DEF\) with \(DF = FE\), the base - angles are equal. Also, since \(DG\) bisects \(\angle FDE\), \(\angle FDG=\angle GDE = 29^{\circ}\).

Step2: Use the angle - sum property of a triangle

We know that in \(\triangle DEF\), \(\angle DFE=180^{\circ}- 2\times\angle FDE\). First, \(\angle FDE = 2\times29^{\circ}=58^{\circ}\) (because \(DG\) bisects \(\angle FDE\)). Then, using the formula for the sum of angles in a triangle \(\angle DFE=180^{\circ}-2\times\angle FDE\). Substitute \(\angle FDE = 58^{\circ}\) into the formula: \(\angle DFE=180^{\circ}- 2\times58^{\circ}\).

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Answer:

\(64^{\circ}\)