Question

question
in δmno, m∠m = 13° and m∠n = 101°. which statement about the sides of δmno must be true?
answer
○ om > no > mn
○ mn > om > no
○ om > mn > no
○ mn > no > om
○ no > mn > om
○ no > om > mn

Explanation:

Step1: Find the third angle

In $\triangle MNO$, the sum of angles is $180^\circ$. Given $m\angle M = 13^\circ$ and $m\angle N = 101^\circ$, so $m\angle O=180 - 13 - 101 = 66^\circ$.

Step2: Relate angles to sides

In a triangle, the larger angle is opposite the longer side. Angles: $\angle N = 101^\circ$ (largest), $\angle O = 66^\circ$, $\angle M = 13^\circ$ (smallest). Opposite sides: $\angle N$ opposite $OM$, $\angle O$ opposite $MN$, $\angle M$ opposite $NO$. So side lengths: $OM$ (opposite $101^\circ$) > $MN$ (opposite $66^\circ$) > $NO$ (opposite $13^\circ$), which is $OM > MN > NO$.

Answer:

The option with "OM > MN > NO" (the second option in the first row of choices)