AX and BX are two adjacent sides of a regular polygon.If angle ABX=1/3 OF angle AXB then the number of sides in the polygon are
Since we are discussing a regular polygon, ABX will be an isosceles triangle and AX = BX. If <ABX = x = <BAX and <AXB = 3x.
x+x+3x = 5x = 180 or x = 36.
<AXB = 36x3 = 108 deg so the exterior angle = 180–108 = 72 deg.
No. of sides of the regular polygon = 360/72 = 5.
So the figure is a regular pentagon.