Question

determine if triangle ijk and triangle lmn are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)
answer attempt 1 out of 2
the triangles similar.

Explanation:

Step1: Find ∠J in △IJK

Sum of angles in a triangle is $180^\circ$.
$\angle J = 180^\circ - 60^\circ - 53^\circ = 67^\circ$

Step2: Find ∠M in △LMN

Sum of angles in a triangle is $180^\circ$.
$\angle M = 180^\circ - 60^\circ - 53^\circ = 67^\circ$

Step3: Match corresponding angles

In △IJK: $\angle I=60^\circ$, $\angle K=53^\circ$, $\angle J=67^\circ$
In △LMN: $\angle L=60^\circ$, $\angle N=53^\circ$, $\angle M=67^\circ$
All corresponding angles are equal.

Answer:

The triangles are similar by the AA (Angle-Angle) similarity criterion (all three corresponding angles are congruent).