Question

How many sides has a regular polygon, each angle of which is of measure 108 degree.

Answer 1

If each interior angle is 108⁰

Then, Each exterior angle =>

e∠ + 108⁰ = 180⁰ (Linear Pair)

e∠ = 180⁰ - 108⁰

e∠ = 72⁰

Each Exterior angle = 72⁰

No. of Sides =       360⁰              

                     Each Exterior Angle

= 360⁰

   108⁰

= 5

So, the polygon has 5 sides and it is a regular pentagon.