Question 921599

A "Regular Polygon" has:

    all sides equal and
    all angles equal.
The Exterior Angle is the angle between any side of a shape,
and a line extended from the next side.

The Interior Angle and Exterior Angle are measured from the same line, so they add up to {{{180}}}°.

{{{Interior_ Angle = 180 - Exterior_ Angle}}}

the sum of

{{{Interior_ Angle = (n-2) * (180 / n)}}} where {{{n}}} is the number of sides

 {{{Exterior_ Angle=360/n}}}   where {{{n}}} is the number of sides

given: polygon has exterior angles that are congruent to its interior angles

then {{{(n-2) * (180 / n) =360/n}}}...........solve for {{{n}}}

{{{(n-2) * 180  =360n/n}}}

{{{(n-2) * 180  =360}}}


{{{n-2 =360/180 }}}


{{{n-2 =2 }}}

{{{n =2+2 }}}

{{{n =4 }}}......the number of sides


The answer has to be "{{{A}}}{{{ Square}}}" because a {{{regular}}} polygon {{{must}}}{{{ have}}} all {{{equal}}}{{{ sides}}} and all {{{equal}}}{{{ angles}}}.

A rectangle(even polygon with {{{4}}} sides)  does not agree with definition of a "Regular Polygon" because it does not have four equal sides.
Only a square agrees with the original definition.