SOLUTION: the floor of a gazebo is in the shape of a regular polygon. The measure of an exterior angle of the gazebo floor is one third the measure of an interior angle. How many sides d

Algebra ->  Polygons -> SOLUTION: the floor of a gazebo is in the shape of a regular polygon. The measure of an exterior angle of the gazebo floor is one third the measure of an interior angle. How many sides d      Log On


   

Question 348945: the floor of a gazebo is in the shape of a regular polygon. The measure of an exterior angle of the gazebo floor is one third the measure of an interior angle.
How many sides does the gazebo have? Show work or explain in words how this was determined.
* There is a diagram to this question.
In words it looks like... if you turn the paper to landscape form, the diagram looks like a k without the bottom \ then turning he paper portrait there is an "x" on the left side if the diagram and "x" over 3 on the right.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the interior/exterior pair are supplementary (they sum to 180º)

so ___ x + 3x = 180º ___ x = 45º

the exterior angles of a polygon sum to 360º

so the number of sides is ___ 360/45