Question

in △nop, m∠n = 101° and m∠o = 10°. which statement about the sides of △nop must be true? answer op > pn > no no > pn > op no > op > pn op > no > pn pn > op > no pn > no > op

Explanation:

Step1: Find the third - angle measure

In a triangle, the sum of interior angles is 180°. Let $\angle P=x$. Then $101^{\circ}+10^{\circ}+x = 180^{\circ}$, so $x=180^{\circ}-(101^{\circ}+10^{\circ})=69^{\circ}$.

Step2: Apply the angle - side relationship

In a triangle, the side opposite the largest angle is the longest and the side opposite the smallest angle is the shortest. $\angle N = 101^{\circ}$ (largest), $\angle P=69^{\circ}$, $\angle O = 10^{\circ}$ (smallest). The side opposite $\angle N$ is $OP$, the side opposite $\angle P$ is $NO$, and the side opposite $\angle O$ is $PN$. So $OP>NO>PN$.

Answer:

OP > NO > PN