Question

△nut
nu = 4.5 cm, ut = 6 cm, nt = 3 cm
arrange the angles from smallest to largest based on their measures.
∠u, ∠t, ∠n
∠t, ∠u, ∠n
∠n, ∠u, ∠t
∠t, ∠n, ∠u

Explanation:

Step1: Recall the triangle - side - angle relationship

In a triangle, the larger the side length, the larger the angle opposite it.

Step2: Compare the side lengths

Given \(NU = 4.5\mathrm{cm}\), \(UT = 6\mathrm{cm}\), \(NT=3\mathrm{cm}\). The order of side lengths from smallest to largest is \(NT

Step3: Determine the order of angles

The angle opposite \(NT\) is \(\angle U\), the angle opposite \(NU\) is \(\angle T\), and the angle opposite \(UT\) is \(\angle N\). So, the order of angles from smallest to largest is \(\angle U,\angle T,\angle N\).

Answer:

\(\angle U,\angle T,\angle N\)