Question

The diagram shows two congruent regular polygons joined together.

Work out the number of sides of each polygon.

Answer 1

Check the picture below.

so we know the interior angles in the polygons is 144°, so

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =144 \end{cases}\implies n(144)=180(n-2) \\\\\\ 144n=180n-360\implies 144n+360=180n \\\\\\ 360=36n\implies \cfrac{360}{36}=n\implies \boxed{10=n}`