Question

Find the degree and radian measure of exterior and interior angle of a regular Octagon.

Answer 1

Octagon:

Number of sides = 8

Number of exterior angles = 8

Sum of exterior angles = 360°

∴ Each exterior angle = ${\displaystyle \frac{360°}{\text{no. of sides}}}$

= ${\displaystyle \frac{360°}{8}}$

= 45°

=${\displaystyle {(45\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{\pi }{4}\right)}^{\text{c}}}$

Interior angle + Exterior angle = 180°

∴ Each interior angle = 180° – 45° = 135°

= ${\displaystyle {(135\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{3\pi }{4}\right)}^{\text{c}}}$