Let's begin with recalling that the sum of the exterior angles of a polygon is always equal to 360^(∘). Using this information, we can find the measure of each exterior angle in a regular octagon. To do this, let's divide 360^(∘) by 8.
360^(∘)/8=45^(∘)
Now, we will mark some of the exterior angles of these octagons. We will focus our reasoning on one quadrilateral, as all of them are congruent figures.
Notice that each angle of a quadrilateral is made from two exterior angles of an octagon. Therefore, each angle of this quadrilateral has a measure of 45^(∘)+ 45^(∘)=90^(∘). Since all sides of the regular octagon are congruent, the sides of quadrilaterals will be also congruent.
Let's recall that the quadrilateral with all four congruent sides and four right angles is a square. Therefore, we can say that all the quadrilaterals are squares.
