The interior angle of a regular polygon is five... - JAMB Mathematics 2023 Question

The relationship between the interior angle (\(I\)) and the exterior angle (\(E\)) of a regular polygon is given by the formula:

\[I = 180^\circ - E\]

Given that the interior angle is five times the size of the exterior angle, we can set up the equation:

\[I = 5E\]

Now, substitute \(180^\circ - E\) for \(I\) in the equation:

\[180^\circ - E = 5E\]

Combine like terms:

\[180^\circ = 6E\]

Solve for \(E\):

\[E = \frac{180^\circ}{6} = 30^\circ\]

So, the exterior angle of the regular polygon is \(30^\circ\).

Now, we know that the exterior angle of a regular polygon is given by \(360^\circ/n\), where \(n\) is the number of sides. Set up the equation:

\[30^\circ = \frac{360^\circ}{n}\]

Solve for \(n\):

\[n = \frac{360^\circ}{30^\circ} = 12\]

So, the polygon has 12 sides, and it is a dodecagon.