Question

which list orders the angles of △rst in order from greatest to least in measure?

∠r, ∠s, ∠t
∠t, ∠s, ∠r
∠s, ∠r, ∠t
∠t, ∠r, ∠s

Explanation:

Step1: Recall the triangle side - angle relationship

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

Step2: Identify the side lengths

In \(\triangle RST\), the side lengths are \(RS = 6\mathrm{cm}\), \(ST=7\mathrm{cm}\), \(RT = 8\mathrm{cm}\).

Step3: Determine the angles opposite the sides

\(\angle T\) is opposite \(RS\), \(\angle R\) is opposite \(ST\), \(\angle S\) is opposite \(RT\).
Since \(RT>ST > RS\), then \(\angle S>\angle R>\angle T\) (by the side - angle relationship in a triangle).

Answer:

\(\angle S,\angle R,\angle T\)