Question

find the measure of an exterior angle of a regular pentagon and an exterior angle of regular decagon what is the ratio between these two angles ​

Answer 1

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

Answer 2

Answer:

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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}

5

540

= 108°

Exterior angle= 180°- 108° = 72°

Decagon has 10 sides

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

10

1440

= 144°

Exterior Angle = 180° - 144° = 36°

∴ Ratio of exterior angle of regular Pentagon to regular Decagon

= 72 : 36

= 2:1