Question

What is the sum of the measures of the interior angles of an octagon?

Answer 1

`1080^@`

Explanation:

To calculate the `color(blue)"sum of the interior angles of a polygon"` in general use.

`color(red)(bar(ul(|color(white)(a/a)color(black)(180^@(n-2))color(white)(a/a)|)))`
where n represents the number of sides of the polygon.

For an octagon with 8 sides, n = 8

`rArr"sum of interior angles"=180^@xx(8-2)`

`=180^@xx6=1080^@`