Question

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

Answer 1

Hexagon:
Number of sides = 6
Number of exterior angles = 6
Sum of exterior angles = 360°

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

= ${\displaystyle \frac{360°}{6}}$

= 60°

= ${\displaystyle {(60\times \frac{\pi }{180})}^{\text{c}}}$

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

Interior angle + Exterior angle = 180°

∴ Each interior angle = 180° – 60° = 120°

= ${\displaystyle {(120\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{2\pi }{3}\right)}^c}$