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∠z < m∠y < m∠x m∠y < m∠z < m∠x m∠x < m∠z < m∠y m∠y < m∠x < m∠z

Explanation:

Step1: Compare the side lengths

Given \(m\geq6\).

• \(XY=m + 8\)
• \(XZ=m-3\)
• \(YZ=2m + 3\)

Let's find the differences:

• \(YZ−XY=(2m + 3)-(m + 8)=m-5\). Since \(m\geq6\), \(m - 5>0\), so \(YZ>XY\)
• \(XY−XZ=(m + 8)-(m - 3)=11>0\), so \(XY>XZ\)

So, \(XZ

Step2: Use the angle - side relationship

In a triangle, the larger side is opposite the larger angle.

• Side \(XZ\) is opposite \(\angle Y\)
• Side \(XY\) is opposite \(\angle Z\)
• Side \(YZ\) is opposite \(\angle X\)

Since \(XZ

Answer:

\(m\angle Y < m\angle Z < m\angle X\)