The limit of the interior angle of a regular | vedclass

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(A) The interior angle of a regular polygon with $n$ sides is given by the formula: $	heta_n = \frac{(n-2) 	imes 180^{\circ}}{n}$.We want to find th

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$\pi$

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(A) The interior angle of a regular polygon with $n$ sides is given by the formula: $	heta_n = \frac{(n-2) 	imes 180^{\circ}}{n}$.We want to find the limit as $n ightarrow \infty$:$\lim_{n ightarrow \infty} 	heta_n = \lim_{n ightarrow \infty} \frac{(n-2) 	imes 180^{\circ}}{n} = \lim_{n ightarrow \infty} (1 - \frac{2}{n}) 	imes 180^{\circ}$.As $n ightarrow \infty$,the term $\frac{2}{n} ightarrow 0$.Therefore,the limit is $(1 - 0) 	imes 180^{\circ} = 180^{\circ} = \pi 	ext{ radians}$.

The limit of the interior angle of a regular polygon of $n$ sides as $n \rightarrow \infty$ is

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