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

The sum of the measures of the interior angles of an octagon is 1080°.

How to see it quickly

Use the interior-angle formula for any 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∘=1080∘.(8-2)\times 180^\circ =6\times 180^\circ =1080^\circ.(8−2)×180∘=6×180∘=1080∘.

So, all 8 interior angles of any octagon together always add up to 1080 degrees.

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