How many sides does a regular polygon have if each of its interior angles is 108°?


Given: A regular polygon's interior angles measure 108°

To find: How many sides does this polygon has


Solution:
The sum of interior angles of a regular polygon of n sides is $(n-2)\times180°$

If each of the interior angles is 108°, then are n interior angles

Sum of interior angles =>$108n = (n-2)180$

Solving for n   

=$180n - 108n$

= $72n = 360$ 

=>$n = \frac{360}{72} = 5$

So the given regular polygon is a pentagon as it has five equal sides.

Updated on: 10-Oct-2022

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