Question

in $\triangle def$, $ef = 13$, $fd = 2$, and $de = 14$. which statement about the angles of $\triangle def$ must be true? answer $mangle e>mangle d>mangle f$ $mangle d>mangle f>mangle e$ $mangle d>mangle e>mangle f$ $mangle e>mangle f>mangle d$ $mangle f>mangle d>mangle e$ $mangle f>mangle e>mangle d$

Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the side opposite an angle, the larger the measure of the angle.

Step2: Identify side - length order

Given \(EF = 13\), \(FD=2\), and \(DE = 14\). The order of side - lengths from largest to smallest is \(DE>EF>FD\).

Step3: Determine angle - measure order

The angle opposite \(DE\) is \(\angle F\), the angle opposite \(EF\) is \(\angle D\), and the angle opposite \(FD\) is \(\angle E\). So the order of angle measures from largest to smallest is \(m\angle F>m\angle D>m\angle E\).

Answer:

\(m\angle F > m\angle D > m\angle E\)