Since △GHI and △LKJ are similar, the corresponding angles are congruent. Therefore, m∠J = m∠G = 30°.
Since the sum of angles in a triangle is 180°, we can calculate m∠K by subtracting the known angle measures from 180°: m∠K = 180° - m∠J - m∠L = 180° - 30° - 30° = 120°.
Since m∠L = 30°, m∠K = 120°, and the sum of angles in a triangle is 180°, m∠J = 30°.
Therefore, the measures of angles J, K, and L are: m∠J = 30°, m∠K = 120°, and m∠L = 30°.