Question

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

Answer 1

Pentagon:
Number of sides = 5
Number of exterior angles = 5
Sum of exterior angles = 360°

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

= ${\displaystyle \frac{360°}{5}}$

= 72°

= ${\displaystyle {(72\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{2\pi }{5}\right)}^{\text{c}}}$

Interior angle + Exterior angle = 180°
∴ Each interior angle = 180° – 72° = 108°

= ${\displaystyle {(108\times \frac{\pi }{180})}^{\text{c}}}$

= ${\displaystyle {\left(\frac{3\pi }{5}\right)}^{\text{c}}}$