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

First, identify vertical angles: ∠MON = ∠POQ = 87°. Use triangle angle sum (180°):
$\angle N = 180^\circ - 40^\circ - 87^\circ = 53^\circ$

Step2: Find ∠P in △PQO

Use triangle angle sum (180°):
$\angle P = 180^\circ - 53^\circ - 87^\circ = 40^\circ$

Step3: Match corresponding angles

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

Answer:

△MNO is similar to △PQO.