Question

△mno and △opq are shown below.
which statement is true?
△mno is similar to △opq.
△mno is not similar to △opq.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Calculate ∠M in △MNO

In right triangle $\triangle MNO$, $\angle N = 90^\circ$, $\angle MON = 59^\circ$.
Sum of angles in a triangle is $180^\circ$, so:
$\angle M = 180^\circ - 90^\circ - 59^\circ = 31^\circ$

Step2: Match corresponding angles

In $\triangle MNO$: $\angle N=90^\circ$, $\angle M=31^\circ$, $\angle MON=59^\circ$
In $\triangle OPQ$: $\angle P=90^\circ$, $\angle POQ=31^\circ$, $\angle Q=180^\circ - 90^\circ - 31^\circ = 59^\circ$
We can see:
$\angle N \cong \angle P$, $\angle M \cong \angle POQ$, $\angle MON \cong \angle Q$
By AA (Angle-Angle) similarity criterion, the triangles are similar.

Answer:

$\triangle MNO$ is similar to $\triangle OPQ$.