Question

find the measure of an exterior angle of a regular pentagon and exterior angle of a decagon ​

Answer 1

Answer:

The Ratio of exterior angle of regular Pentagon to regular Decagon is 2:1

Step-by-step explanation:

The sum of interior angles of a polygon with n sides is = (n-2) * 180

∴ sum of interior angles of regular pentagon is = (5-2) * 180

                                                                              = 3 * 180

                                                                              =540

Pentagon has five interior angles which are all equal

∴ Each interior angle = \frac{540}{5} = 108°

  Exterior angle= 180°- 108° = 72°

Decagon has 10 sides

 Then,   Similarly interior angle = \frac{1440}{10} = 144°

                         Exterior Angle = 180° - 144° = 36°

∴ Ratio of exterior angle of regular Pentagon to regular Decagon

= 72 : 36

= 2:1