Question

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

Explanation:

Step1: Find ∠N in △MNO

Sum of angles in triangle is $180^\circ$.
$\angle N = 180^\circ - 40^\circ - 87^\circ = 53^\circ$

Step2: Find ∠P in △PQO

Sum of angles in triangle is $180^\circ$.
Vertical angles: $\angle POQ = \angle MON = 87^\circ$
$\angle P = 180^\circ - 53^\circ - 87^\circ = 40^\circ$

Step3: Compare triangle angles

In △MNO: $\angle M=40^\circ, \angle N=53^\circ, \angle O=87^\circ$
In △PQO: $\angle P=40^\circ, \angle Q=53^\circ, \angle O=87^\circ$
All corresponding angles are equal.

Answer:

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