What is the smallest angle of rotational symmetry that maps a regular octagon onto itself? enter your answer in the box.

45 Degrees is the smallest angle of rotational symmetry that maps a regular octagon onto itself

Solution-

A regular octagon has 8 equal angles and 8 equal sides.  

When rotating an octagon around its center, 1/8th of a full-circle rotation will cause adjacent sides to coincide on each other.

A circle has 360° and (1/8)th of 360° = 45°.  

Hence, a minimum of 45° rotation counterclockwise or clockwise(as it is symmetric so the order doesn't matter) puts each of the edges over the position where an adjacent edge was located before.

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step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet