Let x=no. of 140 degree angles, then there are 2x 155 degree angles. Therefore the polygon has 3x sides and angles. The total of all the angles is 140x+155(2x)=140x+310x=450x degrees. The total angle sum of an n-gon is 90(2n-4)=180n-360 degrees. So n=3x, and the total angle sum=540x-360=450x, 90x=360, x=4, and n=12. So the polygon has 12 sides.
CHECK
The interior angle of a regular 12-gon is 150°, making the angle sum=1800°. 4×140+8×155=560+1240=1800°. The angle sum of all 12-gons is the same as for a regular 12-gon.