Explanation:
The sum of the measures of the angles of an octagon is given by the formula (n-2) x 180, where n is the number of sides/angles. In the case of an octagon, n = 8, so the sum of the measures of its angles is:
(8-2) x 180 = 6 x 180 = 1080
We are told that the sum of the measures of the seven angles of the octagon is 1000, so we can set up an equation to find the measure of the eighth angle:
1000 + x = 1080
where x is the measure of the eighth angle.
Solving for x, we get:
x = 1080 - 1000 = 80
Therefore, the measure of the eighth angle of the octagon is 80 degrees.