the lengths of the sides of triangle xyz are written in terms of the variable m, where m ≥ 6. which is…

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

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

Answer

Explanation:

Step1: Compare side - lengths

Given side - lengths $m - 3$, $m + 8$, and $2m+3$ with $m\geq6$. First, find the difference between $m + 8$ and $m - 3$: $(m + 8)-(m - 3)=m + 8 - m+3 = 11>0$, so $m + 8>m - 3$. Next, find the difference between $2m + 3$ and $m + 8$: $(2m + 3)-(m + 8)=2m+3 - m - 8=m - 5$. Since $m\geq6$, $m - 5>0$, so $2m + 3>m + 8$. So the order of side - lengths from smallest to largest is $m - 3<m + 8<2m + 3$.

Step2: Use the angle - side relationship in a triangle

In a triangle, the smallest angle is opposite the shortest side and the largest angle is opposite the longest side. Side $XZ=m - 3$ is opposite $\angle Y$, side $XY=m + 8$ is opposite $\angle Z$, and side $YZ = 2m+3$ is opposite $\angle X$. So $m\angle Y<m\angle Z<m\angle X$.

Answer:

$m\angle Y<m\angle Z<m\angle X$