SOLUTION: Please help me with this problem that I can't figure out. Thank you so much. A regular polygon has exterior angles that are congruent to its interior angles. How many sides does

Algebra ->  Polygons -> SOLUTION: Please help me with this problem that I can't figure out. Thank you so much. A regular polygon has exterior angles that are congruent to its interior angles. How many sides does      Log On


   

Question 921599: Please help me with this problem that I can't figure out. Thank you so much.
A regular polygon has exterior angles that are congruent to its interior angles. How many sides does the polygon have?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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+=+%28n-2%29+%2A+%28180+%2F+n%29 where n is the number of sides
Exterior_+Angle=360%2Fn where n is the number of sides
given: polygon has exterior angles that are congruent to its interior angles
then %28n-2%29+%2A+%28180+%2F+n%29+=360%2Fn...........solve for n
%28n-2%29+%2A+180++=360n%2Fn
%28n-2%29+%2A+180++=360

n-2+=360%2F180+

n-2+=2+
n+=2%2B2+
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.