  In this note we sharpen the lower bound from [LLP10] on the spectrum of the
2D Schroedinger operator with a delta-interaction supported on a planar angle.
Using the same method we obtain the lower bound on the spectrum of the 2D
Schroedinger operator with a delta-interaction supported on crossing straight
lines. The latter operators arise in the three-body quantum problem with
delta-interactions between particles.
