The angles of a pentagon are in arithmetic progression. One of the angles, in degrees, must be
Answers
109..........i think this is the correct ans
The least angle is 120 degrees.
The minimum number of sides required to form a polygon is 3.
If the required polygon is of 3 sides, then the angles of the polygon will be 120, 130 and 140 as they must be in AP with common difference 10 degrees.
Sum of angles = 390 degrees.
But, a polygon of 3 sides must have sum of its angles as 180 degrees.
If the required polygon is of 4 sides, then the angles will be 120, 130, 140 and 150 degrees.
Sum of angles = 540 degrees.
But, a polygon of 4 sides must have sum of its angles 360 degrees.
If the required polygon is of 5 sides, then the angles will be 120, 130, 140, 150 and 160 degrees.
Sum of angles = 700 degrees.
But, a polygon of 5 sides must have sum of its angles 540 degrees.
If the required polygon is of 6 sides, then the angles will be 120, 130, 140, 150, 160 and 170 degrees.
Sum of angles = 870 degrees.
But, a polygon of 6 sides must have sum of its angles 720 degrees.
The polygon cannot be of 7 sides because that will mean one angle must be 180 degrees which is not possible.
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