To solve the problem, we can use proportions. Since the central angle for running shoes is 80 degrees, we know that the ratio of running shoes sold to total shoes sold is 80/360. This is because the total number of degrees in a circle is 360. Therefore, we can set up the proportion:
80/360 = 200/x
where x is the total number of shoes sold. Solving for x, we get:
x = (360 * 200)/80
x = 900
Therefore, the total number of shoes sold is 900.