Question

Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?

Answer 1

Step-by-step explanation:

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 = = 108°

Exterior angle= 180°- 108° = 72°

Decagon has 10 sides

Then, Similarly interior angle = = 144°

Exterior Angle = 180° - 144° = 36°

∴ Ratio of exterior angle of regular Pentagon to regular Decagon

= 72 : 36

= 2:1

Answer 2

Answer:

2:1

Step-by-step explanation:

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

= sum of interior angle of a regular Pentagon is= (5-2)*180=3*180= 540

Pentagon has 5 interior angle which are all equal

= Each interior angle =108 degree

Each exterior angle = 180degree - 108 degree= 72 degree

Decagon has 10 sides

Thus, similarly interior angle = 144degree

Exterior angle =180degree- 144degree = 36degree

= Ratio of a exterior angle of regular Pentagon to regular decagon=

72:36 =2:1