Question

This is a regular polygon.Name:sum of interior:1 Interior:Sum of exterior:1 Exterior:

Answer 1

A regular polygon with 7 sides is a heptagon.

To find the measure the interior angle (I):

`I=(180n-360)/(n)`

Where n is the number of sides (7):

`\begin{gathered} I=(180\cdot7-360)/(7) \\ I=(1260-360)/(7)=(900)/(7) \\ I=128.57\degree \end{gathered}`

And the sum of the interior angles is:

`\begin{gathered} Si=n\cdot I \\ Si=7\cdot128.57 \\ Si=900\degree \end{gathered}`

The sum of the exterior angles (Se) is 360°.

And the sum of one exterior angle (E):

`\begin{gathered} E=(360)/(n) \\ E=(360)/(7) \\ E=51.43\degree \end{gathered}`

In summary:

Name: Heptagon

Sum of interior: 900°

1 Interior: 128.57°

Sum of exterior: 360°

1 Exterior:​ 51.43°