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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.
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