Question

$\triangle mno$ and $\triangle pnr$ are shown below.
which statement is true?
$\triangle mno$ is similar to $\triangle pnr$.
$\triangle mno$ is not similar to $\triangle pnr$.
there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Find ∠MON in △MNO

In right △MNO, sum of angles is $180^\circ$.
$\angle MON = 180^\circ - 90^\circ - 31^\circ = 59^\circ$

Step2: Find ∠MPR in △PNR

In right △PNR, sum of angles is $180^\circ$.
$\angle MPR = 180^\circ - 90^\circ - 69^\circ = 21^\circ$

Step3: Compare triangle angle sets

△MNO angles: $31^\circ, 90^\circ, 59^\circ$
△PNR angles: $21^\circ, 90^\circ, 69^\circ$
No matching 3-angle sets.

Answer:

$\Delta MNO$ is not similar to $\Delta PNR$.