Question

question in △efg, fg = 20, ge = 19, and ef = 15. which statement about the angles of △efg must be true? answer m∠f > m∠e > m∠g m∠g > m∠f > m∠e m∠e > m∠g > m∠f m∠e > m∠f > m∠g m∠g > m∠e > m∠f m∠f > m∠g > m∠e

Explanation:

Step1: Recall angle - side relationship in a triangle

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Step2: Identify the longest and shortest sides

Given \(FG = 20\), \(GE=19\), and \(EF = 15\). The longest side is \(FG\), the middle - length side is \(GE\), and the shortest side is \(EF\).

Step3: Determine the order of angles

The angle opposite \(FG\) is \(\angle E\), the angle opposite \(GE\) is \(\angle F\), and the angle opposite \(EF\) is \(\angle G\). So, \(m\angle E>m\angle F > m\angle G\).

Answer:

\(m\angle E>m\angle F > m\angle G\) (corresponding to the option where this inequality is stated)