Question

a regular polygon has exterior angles measuring 40 degrees how many sides does the polygon have

Answer 1

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

Since the polygon is regular, each interior angle is therefore 

$\frac{n - 2}{n} \times {180}^{o}$. This should be equal to 

${180}^{o} - {40}^{o}$

∘ so you can write an equation and solve for nn.

That is not the fastest solution, but your

$(n−2)× {180}^{o} (n−2)×{180}^{o}$

 is the sum of the interior angles.

A regular polygon with an exterior angle measure of 40 degrees has nine sides. Every polygon's exterior angle sum equals 360.

$So \: \frac{360}{40} \: equals \: nine.$