Problems(1)
Construct a square on one side of an equilateral triangle. One on non-adjacent side of the square, construct a regular pentagon, as shown. One a non-adjacent side of the pentagon, construct a hexagon. Continue to construct regular polygons in the same way, until you construct an octagon. How many sides does the resulting polygon have?[asy]
defaultpen(linewidth(0.6));
pair O=origin, A=(0,1), B=A+1*dir(60), C=(1,1), D=(1,0), E=D+1*dir(-72), F=E+1*dir(-144), G=O+1*dir(-108);
draw(O--A--B--C--D--E--F--G--cycle);
draw(O--D, dashed);
draw(A--C, dashed);[/asy]<spanclass=′latex−bold′>(A)</span>21<spanclass=′latex−bold′>(B)</span>23<spanclass=′latex−bold′>(C)</span>25<spanclass=′latex−bold′>(D)</span>27<spanclass=′latex−bold′>(E)</span>29