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

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) (Show Source): You can put this solution on YOUR website!
the interior/exterior pair are supplementary (they sum to 180�)

so ___ x + 3x = 180� ___ x = 45�

the exterior angles of a polygon sum to 360�

so the number of sides is ___ 360/45
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