An interior designer uses a regular pentagon shape for a tabletop. What is the measure of each interior angle?
$108^0$
A regular polygon has all sides and all interior angles equal, so each interior angle is the total interior-angle sum shared equally among the vertices.
The sum of the interior angles of an \(n\)-sided polygon is \((n-2)\times 180^\circ\), so each interior angle \(= \frac{(n-2)\times 180^\circ}{n}\).
A pentagon has \(n = 5\) sides.
Substituting: \(= \frac{(5-2)\times 180^\circ}{5} = \frac{3 \times 180^\circ}{5}\).
\(= \frac{540^\circ}{5} = 108^\circ\).
Key concept: for a regular polygon, interior angle \(= \frac{(n-2)180^\circ}{n}\); equivalently \(180^\circ\) minus the exterior angle \(\frac{360^\circ}{5}=72^\circ\) also gives \(108^\circ\).
Hence each interior angle of the pentagonal tabletop is 108°.
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