Question

In △ PQR, QR=15, RP=16 , and PQ=18. Which statement about the angles of △ PQR must be true?

a. m∠ P>m∠ R>m∠ Q
b. m∠ P>m∠ Q>m∠ R
c. m∠ R>m∠ Q>m∠ P
d. m∠ R>m∠ P>m∠ Q
e. m∠ Q>m∠ R>m∠ P
f. m∠ Q>m∠ P>m∠ R

Answer 1

Given △ PQR with side lengths PQ=18, RP=16, and QR=15, the correct angle relationship is m∠ Q > m∠ P > m∠ R, with angle Q as the largest and angle R as the smallest.

Step-by-step explanation:

The question concerns determining which statement about the angles of △ PQR must be true, given the lengths of the sides. To solve this, we need to recall the properties of triangles. The angle opposite the longest side is the largest angle, and the angle opposite the shortest side is the smallest angle. In △ PQR, PQ is the longest side (18), followed by RP (16), and QR is the shortest (15). Therefore, the largest angle will be opposite PQ, and the smallest angle will be opposite QR.

Based on this, the correct statement should be that m∠ Q > m∠ P > m∠ R because angle Q is opposite the longest side (PQ), and angle R is opposite the shortest side (QR). Hence, the correct answer to the question is option f, which corresponds to m∠ Q > m∠ P > m∠ R.