Question

what is the sum of 7 of the interior angles of a regular octagon

Answer 1

The sum of all the eight interior angles of a regular octagon is first obtained using the general formula:

$(n-2)\times180^o$

where n = number of sides of the regular polygon

For a regular octagon, n = 8, and so we have:

$(8-2)\times180^o$$6\times180^o$$1080^o$

Now, we divide this total sum by the number of sides of the regular octagon in order to obtain the measure of an individual interior angle of the octagon, as follows:

$\frac{1080^{o^{}}}{n}$$\frac{1080^o}{8}=135^o$

Now, to find the sum of 7 interior angles of a regular octagon, we simply multiply an individual interior angle of the octagon by 7, as follows:

$\text{Sum of 7 interior angles = 7}\times135=945^o$

Therefore, the sum of 7 of the interior angles of a regular octagon is 945 degrees