Find the measure of each interior angle of a regular octagon.
Tripura Public Service Commission - 2019,
Answer: D
Each interior angle of a regular octagon is 135°.
The sum of the interior angles of an \(n\)-sided polygon is \((n - 2) \times 180^\circ\). For an octagon, \(n = 8\).
\[ \begin{aligned} \text{sum} &= 6 \times 180^\circ = 1080^\circ \\ \text{each} &= 1080^\circ \div 8 = 135^\circ \end{aligned} \]
Quicker: each exterior angle is \(360^\circ \div 8 = 45^\circ\), and \(180^\circ - 45^\circ = 135^\circ\). 108° is the angle of a regular pentagon, 120° of a hexagon and 150° of a regular 12-sided polygon.
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