Question

find the largest angle of $\triangle wxy$. assume that $a$ is a positive number.

Explanation:

Step1: Compare side lengths

Since \(a>0\), \(28a > 11a\). Side \(XY=28a\), side \(WX=11a\). In a triangle, longer sides correspond to larger opposite angles. The angle opposite \(XY\) is \(\angle W\), and the angle opposite \(WX\) is \(\angle Y\). So \(\angle W > \angle Y\).

Step2: Analyze given angle

We know \(\angle X = 92^\circ\). The sum of angles in a triangle is \(180^\circ\), so \(\angle W + \angle Y = 180^\circ - 92^\circ = 88^\circ\).

Step3: Identify largest angle

Since \(\angle W + \angle Y = 88^\circ\), both \(\angle W\) and \(\angle Y\) are less than \(88^\circ\), which is smaller than \(92^\circ\).

Answer:

$\angle X$ (or $92^\circ$)