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Two sides of a regular pentagon are produced to meet. Calculate the size of the new angle formed.

User Abin
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so let's check how much is each interior angle in the pentagon first.


\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\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108

Check the picture below.

Two sides of a regular pentagon are produced to meet. Calculate the size of the new-example-1
User Atyz
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