Question

which side is the shortest?
both \\( ef \\) and \\( de \\)
\\( de \\)
\\( df \\)
\\( ef \\)

Explanation:

Step1: Find the measure of angle \( E \)

The sum of angles in a triangle is \( 180^{\circ} \). So, \( \angle E=180^{\circ}-\angle F - \angle D \).
Substitute \( \angle F = 58^{\circ} \) and \( \angle D=62^{\circ} \).
\( \angle E=180^{\circ}-58^{\circ}-62^{\circ}=60^{\circ} \).

Step2: Recall the side - angle relationship in a triangle

In a triangle, the side opposite the smaller angle is shorter.
We have \( \angle F = 58^{\circ}<\angle E = 60^{\circ}<\angle D=62^{\circ} \).
The side opposite \( \angle F \) is \( DE \), the side opposite \( \angle E \) is \( DF \), and the side opposite \( \angle D \) is \( EF \).

Answer:

\(\overline{DE}\)