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)*180^o`

where n = number of sides of the regular polygon

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

`(8-2)*180^o`
`6*180^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}`
`(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}*135=945^o`

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