Since triangles \( \triangle GHI \) and \( \triangle LKJ \) are similar (denoted by \( \triangle GHI \sim \triangle LKJ \)), the corresponding angles of the triangles are equal.
First, we need to find the measure of angle \( J \) in triangle \( LKJ \) which corresponds to angle \( G \) in triangle \( GHI \): \[ m\angle G = 30^\circ \implies m\angle L = 30^\circ \]
Next, we find angle \( K \) which corresponds to angle \( H \): \[ m\angle H = 80^\circ \implies m\angle K = 80^\circ \]
Finally, we find angle \( J \) which corresponds to angle \( I \): \[ m\angle I = 70^\circ \implies m\angle J = 70^\circ \]
So, the measures of angles \( J \), \( K \), and \( L \) are: \[ m\angle L = 30^\circ, \quad m\angle K = 80^\circ, \quad m\angle J = 70^\circ \]