Question

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

Answer 1

Answer:

$135^\circ$

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 $60^\circ$.

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:

$\dfrac{n-2}{n}\times 180^\circ$

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

Value of Interior angle in a regular octagon:

$\dfrac{8-2}{8}\times 180^\circ=\dfrac{6}{8}\times 180^\circ=\bold{135^\circ}$

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