Question

in δpqr, m∠p = 89° and m∠q = 31°. which list has the sides of δpqr in order from longest to shortest? answer
○ pq, rp, qr
○ rp, pq, qr
○ qr, pq, rp
○ rp, qr, pq
○ pq, qr, rp
○ qr, rp, pq

Explanation:

Step1: Find the measure of angle R

The sum of angles in a triangle is 180°. So, $m\angle R=180^{\circ}-m\angle P - m\angle Q$. Substituting $m\angle P = 89^{\circ}$ and $m\angle Q=31^{\circ}$, we get $m\angle R=180-(89 + 31)=60^{\circ}$.

Step2: Recall the angle - side relationship in a triangle

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

Step3: Determine the order of sides

The side opposite $\angle P$ is $QR$, the side opposite $\angle R$ is $PQ$, and the side opposite $\angle Q$ is $RP$. So the order of sides from longest to shortest is $QR, PQ, RP$.

Answer:

QR, PQ, RP