Question

the lengths of the sides of triangle xyz are written in terms of the variable m, where m ≥ 6. which is correct regarding the angles of the triangle? m∠x < m∠z < m∠y m∠y < m∠z < m∠x m∠y < m∠x < m∠z m∠z < m∠y < m∠x

Explanation:

Step1: Compare the side lengths

Since \(m\geq6\),
For \(m - 3\) and \(m + 8\):
\((m + 8)-(m - 3)=m+8 - m + 3=11>0\), so \(m + 8>m - 3\).
For \(m + 8\) and \(2m+3\):
\((2m + 3)-(m + 8)=2m+3 - m - 8=m - 5\), when \(m\geq6\), \(m-5\geq1>0\), so \(2m + 3>m + 8\).

So the order of side lengths is \(m-3

Step2: Use the triangle - angle - side relationship

In a triangle, the larger side is opposite the larger angle.
The side opposite \(\angle Y\) is \(XZ\), the side opposite \(\angle Z\) is \(XY\), and the side opposite \(\angle X\) is \(YZ\).
Since \(XZ

Answer:

\(m\angle Y