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?
options:
○ ( mangle x < mangle z < mangle y )
○ ( mangle y < mangle z < mangle x )
○ ( mangle y < mangle x < mangle z )
○ ( mangle z < mangle y < mangle x )
(image of triangle xyz with sides: xy = m + 8, xz = m - 3, yz = 2m + 3)

Explanation:

Step1: Assign sides to angles

Side opposite ∠X: \(2m + 3\); opposite ∠Y: \(m - 3\); opposite ∠Z: \(m + 8\)

Step2: Compare side lengths (m ≥ 6)

• \(m - 3 ≤ 3\) (when m=6: 3), \(m + 8 ≥14\), \(2m +3 ≥15\)
• Order of sides: \(m -3 < m +8 < 2m +3\)

Step3: Relate sides to angles

Smallest side ↔ smallest angle; largest side ↔ largest angle
So \(∠Y < ∠Z < ∠X\)

Answer:

∠Y < ∠Z < ∠X (corresponding to the option "m∠Y < m∠Z < m∠X")