What is the interior angle of a regular octagon of side length 2 cm?

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NDA (Held On: 18 Apr 2021) Maths Previous Year paper
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  1. \(\dfrac{\pi}{2}\)
  2. \(\dfrac{3\pi}{4}\)
  3. \(\dfrac{3\pi}{5}\)
  4. \(\dfrac{3\pi}{8}\)

Answer (Detailed Solution Below)

Option 2 : \(\dfrac{3\pi}{4}\)
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Detailed Solution

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Concept:

The interior angle of a regular polygon is given by:  

\(\rm (n - 2) \times \frac{180^{\circ}}{n}\)

Where, n = number of sides

Interior Angle = 180°- Exterior Angle

Calculation:

Regular Octagon has 8 sides

so, n = 8

Interior Angle

\(\rm (n - 2) \times \frac{180^{\circ}}{n}\)

\(\rm (8 - 2) \times \frac{180^{\circ}}{8}\)

\(\rm 6 \times \frac{180^{\circ}}{8}\)

\(\dfrac{3\pi}{4}\)

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