Question

1. use the information in the figure. if $mangle f = 116$, find $mangle e$. 58 32 116 64

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle DEF \) is isosceles (two sides are equal). So \( \angle D=\angle E \).

Step2: Use the triangle angle - sum property

The sum of angles in a triangle is \( 180^{\circ} \). Let \( \angle E = x \), \( \angle D=x \), and \( \angle F = 116^{\circ} \). Then \( x + x+116^{\circ}=180^{\circ} \).

Step3: Solve the equation

Combine like terms: \( 2x=180^{\circ}-116^{\circ} \). So \( 2x = 64^{\circ} \). Divide both sides by 2: \( x=\frac{64^{\circ}}{2}=32^{\circ} \).

Answer:

32