Question

in △fgh, gh = 16, hf = 18, and fg = 20. which list has the angles of △fgh in order from smallest to largest? answer: m∠f, m∠g, m∠h; m∠f, m∠h, m∠g; m∠g, m∠f, m∠h; m∠h, m∠g, m∠f; m∠h, m∠f, m∠g; m∠g, m∠h, m∠f

Explanation:

Step1: Recall angle - side relationship

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

Step2: Identify shortest and longest sides

Given \(GH = 16\), \(HF=18\), and \(FG = 20\). The shortest side is \(GH\), the middle - length side is \(HF\), and the longest side is \(FG\).

Step3: Determine corresponding angles

The angle opposite \(GH\) is \(\angle F\), the angle opposite \(HF\) is \(\angle G\), and the angle opposite \(FG\) is \(\angle H\). So the order of angles from smallest to largest is \(\angle F,\angle G,\angle H\) or \(m\angle F,m\angle G,m\angle H\).

Answer:

A. \(m\angle F, m\angle G, m\angle H\)