Question

in △pqr, m∠p = 34° and m∠q = 22°. which list has the sides of △pqr in order from shortest to longest? answer: qr, rp, pq; pq, rp, qr; rp, pq, qr; rp, qr, pq; pq, qr, rp; qr, pq, rp

Explanation:

Step1: Find angle R

In a triangle, the sum of interior angles is 180°. So, $m\angle R=180^{\circ}-m\angle P - m\angle Q$. Substituting $m\angle P = 34^{\circ}$ and $m\angle Q=22^{\circ}$, we get $m\angle R=180^{\circ}-34^{\circ}-22^{\circ}=124^{\circ}$.

Step2: Recall angle - side relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest. The order of angles from smallest to largest is $\angle Q<\angle P<\angle R$. The side opposite $\angle Q$ is $RP$, the side opposite $\angle P$ is $QR$, and the side opposite $\angle R$ is $PQ$.

Answer:

RP, QR, PQ