Question

in $\triangle pqr$, $mangle p = 101^{circ}$ and $mangle q = 52^{circ}$. which statement about the sides of $\triangle pqr$ must be true?

Explanation:

Step1: Find angle R

The sum of angles in a triangle is 180°. So, $m\angle R=180^{\circ}-m\angle P - m\angle Q$. Given $m\angle P = 101^{\circ}$ and $m\angle Q=52^{\circ}$, then $m\angle R=180^{\circ}- 101^{\circ}-52^{\circ}=27^{\circ}$.

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 smallest angle is $\angle R = 27^{\circ}$, the side opposite it is $PQ$. The largest angle is $\angle P=101^{\circ}$, the side opposite it is $QR$. And the side opposite $\angle Q = 52^{\circ}$ is $RP$. So, $PQ

Answer:

PQ < RP < QR