If the ratio of the perimeter of octagon ABCDEFGH to the perimeter of octagon STUVWXYZ is 1:1, which of the following must be true?

Question

Accepted Answer

The number of sides of a polygon determines the sum of the interior angles of the polygon. The sum of the interior angles of any octagon is 180(8 – 2) = 180(6) = 1,080°. These two octagons are not necessarily similar or congruent, although they could be. The ratio of AB to ST could be 1:1, but there could also be no ratio between the sides of ABCDEFGH and STUVWXYZ. No one side of ABCDEFGH must equal one side of STUVWXYZ. However, since both are octagons, the sums of their interior angles must be equal.

Want a deeper, personalized explanation?

Related questions