for a regular polygon, sum of exterior angle is \(360^{\circ}\)
thus, one ext. angle \(=\frac{360^{\circ}}{\mathrm{n}}\)
where \(\mathrm{n}\) is number of sides
let one angle \(=24^{\circ}\)
then \(24^0=\frac{360^{\circ}}{\mathrm{n}}\)
or \(\mathrm{n}=\frac{360^{\circ}}{24}=15\)
again, let \(\theta=180^{\circ}\)
thus \(\mathrm{n}=\frac{360^{\circ}}{15}=24\) sides
and
again let \(\theta=180^{\circ}\)
\(\mathrm{n}=\frac{360^{\circ}}{180^{\circ}}=2\) sides
we note that a polygon cannot have 2 sides, hence, \(180^{\circ}\) is not an exterior angle of a polygon