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Question
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Solution
\[\text{ Sum of the interior angles of the polygon }= \left( n - 2 \right)\pi\]
Number of sides in the octagon = 8
\[ \therefore \text{ Sum of the interior angles of the octagon }= \left( 8 - 2 \right)\pi = 6\pi\]
\[\text{ Each angle of the octagon }= \frac{\text{Sum of the interior angles of the polygon }}{\text{ Number of sides }} = \frac{6\pi}{8} = \frac{3\pi}{4}\text{ rad }\]
\[\text{ Each angle of octagon }= \left( \frac{3\pi}{4} \times \frac{180}{\pi} \right)^\circ= 135^\circ\]
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