Question 676557
This sequence is synonymous with the Fibonacci sequence: 1,1,2,3,5,8,...
In other words, this sequence pertains to the number of lines two numbers behind plus the number of lines directly behind. 
So, 1 line plus 1 line is an angle. An angle plus the line before is 3 lines, or a triangle. A triangle and two more lines is equal to five total lines, which is a pentagon. And 5+3= 8 lines...

Thus, the next object in this patten is an octagon, because it has 8 lines.