SOLUTION: The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex.How many sides does the polygon h
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Question 188976: The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex.How many sides does the polygon have? Answer by solver91311(24713) (Show Source):
The sum of the measures of the exterior angles of a polygon is always 360 degrees. This makes perfect sense because if you walked all the way around the polygon, the sum of the measures of the angles of all the turns you made would have to be 360 degrees because you would end up facing in the same direction that you started.
The sum of the measures of the internal angles of a polygon is given by:
Where n is the number of sides. This also makes sense because if you draw diagonals to all non-adjacent vertices from one vertex, you will create n - 2 triangles, each of which has a sum of interior angles of 180 degrees.
If the sum of the measures of the interior angles is equal to five times the sum of the measures of the exterior angles, then:
