SOLUTION: The angles of a polygon are 172,164,156and are in arithematic sequence.Find the sequence of exterior angles and the number of sides.
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Question 1118114: The angles of a polygon are 172,164,156and are in arithematic sequence.Find the sequence of exterior angles and the number of sides.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The sum of the measures of an interior angle and the corresponding exterior angle is 180 degrees. So the exterior angles of the polygon form the arithmetic sequence 8, 16, 24, ....
The sum of the exterior angles of any polygon is 360. So
8+16+24+...+8n = 360
The sum of an arithmetic sequence is the number of terms, multiplied by the average of all the terms, which is the same as the average of the first and last terms:
By inspection, n = 9
The polygon has 9 sides.
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