Question

list the angle measures of △hij in order from smallest to largest. assume that x is a positive number. m∠□ < m∠□ < m∠□

Explanation:

Step1: Compare the side lengths

In a triangle, the larger the side length, the larger the angle opposite it.
We have side lengths \(IJ = 31x\), \(IH=14x\), and \(JH\).
Since \(14x<31x\), and by triangle side - length relationships (the sum of two sides \(a + b>c\), \(a + c>b\), \(b + c>a\)), we know that \(IH< IJ\).

Step2: Determine the angles opposite the sides

The angle opposite \(IH\) is \(\angle J\), the angle opposite \(IJ\) is \(\angle H\), and we know \(\angle I = 91^{\circ}\)

Since \(IH< IJ\), then \(m\angle J

Step3: Order the angles

We know that the sum of angles in a triangle is \(180^{\circ}\). Let's assume the angles are \(\angle J\), \(\angle H\), \(\angle I\)
Since \(m\angle J

Answer:

\(m\angle J