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: Calculate side - lengths

Given \(m = 6\).
Side \(XY=m + 8=6 + 8 = 14\).
Side \(YZ=2m+3=2\times6 + 3=12 + 3=15\).
Side \(XZ=m - 3=6 - 3 = 3\).

Step2: Use the angle - side relationship

In a triangle, the larger the side length, the larger the angle opposite it.
The order of side - lengths from smallest to largest is \(XZThe angles opposite these sides are \(\angle Y,\angle Z,\angle X\) respectively.
So the order of angles from smallest to largest is \(m\angle Y

Answer:

\(m\angle Y