Answer:
[tex]135^\circ[/tex]
Step-by-step explanation:
Given that, a regular octagon is to be constructed.
To find:
Each angle in the octagon = ?
Solution:
We know that a regular triangle (polygon with 3 sides) has an interior angle of [tex]60^\circ[/tex].
And a regular quadrilateral (square) has an interior angle of [tex]90^\circ[/tex].
Therefore, formula for interior angle of a regular polygon with [tex]n[/tex] number of sides can be given as:
[tex]\dfrac{n-2}{n}\times 180^\circ[/tex]
For an octagon, we have [tex]n=8[/tex].
Value of Interior angle in a regular octagon:
[tex]\dfrac{8-2}{8}\times 180^\circ=\dfrac{6}{8}\times 180^\circ=\bold{135^\circ}[/tex]
Kindly refer to the attached image for the angle of [tex]135^\circ[/tex]
