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Question

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

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Solution

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.


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