Question

which list orders the angle measures of triangle pqr from least to greatest?

\\(\angle r, \angle p, \angle q\\)
\\(\angle r, \angle q, \angle p\\)
\\(\angle p, \angle r, \angle q\\)
\\(\angle p, \angle q, \angle r\\)

Explanation:

Identify the side lengths and opposite angles

The side lengths of \(\triangle PQR\) are:

• \(PQ = 2.8\) (opposite to \(\angle R\))
• \(PR = 3\) (opposite to \(\angle Q\))
• \(QR = 3.2\) (opposite to \(\angle P\))

Order the side lengths from least to greatest

$$ 2.8 < 3 < 3.2 $$

Substituting the side names:

$$ PQ < PR < QR $$

Apply the side-angle relationship to order the angles

Since the smallest side is opposite the smallest angle and the largest side is opposite the largest angle:

$$ \angle R < \angle Q < \angle P $$

Answer:

• \(\angle R\), \(\angle P\), \(\angle Q\)
• \(\angle R\), \(\angle Q\), \(\angle P\) (Correct answer)
• \(\angle P\), \(\angle R\), \(\angle Q\)
• \(\angle P\), \(\angle Q\), \(\angle R\)