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Angle Sum of Polygon Theory
![The angle sum of an \(n\) sided polygon is given by the formula: $$S=180(n-2).$$ The size of an angle in a \(n\) sided regular polygon (all sides and angles equal) is given by $$\theta=\frac{180(n-2)}{n}$$ \begin{multicols}{2} \textbf{Example 1}\\ Find the angle sum of a pentagon \((n=5)\)\\ \textbf{Example 1 solution}\\[2pt] \(\begin{aligned} S & =180(5-2) \\ & =540^{\circ} \end{aligned}\) \columnbreak \textbf{Example 2}\\ Find the size of an angle in a regular pentagon.\\ \textbf{Example 2 solution}\\[3pt] \(\begin{aligned} \theta & =\frac{180(5-2)}{5} \\ & =\frac{540^{\circ}}{5} \\ & =108^{\circ} \end{aligned}\) \end{multicols}](/media/l21lhjt0/9218.png)
NSW Y8 Maths Geometry Angle Sum of Polygon
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