Question

To construct a regular octagon, what measure would be necessary for each interior angle? Construct an angle of that measure.

Answer 1

`135^\circ`

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
`60^\circ`.

And a regular quadrilateral (square) has an interior angle of
`90^\circ`.

Therefore, formula for interior angle of a regular polygon with
`n` number of sides can be given as:

`(n-2)/(n)* 180^\circ`

For an octagon, we have
`n=8`.

Value of Interior angle in a regular octagon:

`(8-2)/(8)* 180^\circ=(6)/(8)* 180^\circ=\bold{135^\circ}`

Kindly refer to the attached image for the angle of
`135^\circ`