Question 205368
if a polygon has x sides, then each angle of this polygon is:
180 - (360/x)
the angle sum of this polygon 
= x * (180 - (360/x))
= 180x - 360


let:
number of smaller polygon's side = a
angle sum of smaller polygon = 180a - 360
number of larger polygon's side = b
angle sum of larger polygon = 180b - 360


b = 3a
180b - 360 = 4 * (180a - 360)
180*(3a) - 360 = 720a - 1440
540a - 360 = 720a - 1440
1440 - 360 = 720a - 540a
1080 = 180a
a = 1080/180 = 6


so, the smaller polygon has 6 sides