Draw the lines connecting the bases of the points. The points form isosceles triangles with vertex angle of 40 degrees and so base angles of (180- 40)/2= 70 degrees. By symmetry, that forms a square which has angles of 90 degrees. The entire circle around such a point the is divided into four angels: the two 70 degree angles at the base of the two consectutive points, the right angle in the square, and the external angle. Calling the measure of the external angle $\theta$, we have $70+ 70+ 90 +\theta= 230+ \theta= 360$ so $\theta= 360- 230= 130$ degrees.