if in a rectangle, four congruent right-angled triangles are cut from the corners to form a regular octagon.Then will the interior angle of regular octagon be equal to 135 degrees?

Expert Answers
embizze eNotes educator| Certified Educator

A regular polygon is defined as an equiangular,equilateral polygon. Since the sum of the interior angles of any octagon is (8-2)(180)=1080, then each angle will be 1080/8=`135^@` .


So if the resulting octagon is regular, then each interior angle will be `135^@`


Note that you can cut an equilateral octagon from a rectangle that is not regular. Start with a 12x12 square, and cut 3-4-5 right triangles from the corners. The sides of the octagon will all have length 5, but the angles will be different.

Likewise, you can cut an equiangular octagon that is not regular. Start with a 12x20 rectangle, and cut out `4"x"4"x"4sqrt(2)` triangles from the corners. All interior angles will be `135^@` (the exterior angles are all `45^@` since the triangles were isosceles) but the side lengths differ.