The sum of the measures of the interior angles of an octagon is 1,080 degrees. This is calculated using the formula for the sum of the interior angles of a polygon: (n−2)×180∘(n-2)\times 180^\circ (n−2)×180∘, where nnn is the number of sides. For an octagon (n=8n=8n=8):

(8−2)×180∘=6×180∘=1,080∘(8-2)\times 180^\circ =6\times 180^\circ =1,080^\circ (8−2)×180∘=6×180∘=1,080∘

Therefore, the total sum is 1,080°