Question 1210523: The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $148^\circ$. If the polygon has 3 sides, then find the smallest angle, in degrees.
Answer by ikleyn(53646)   (Show Source):
You can put this solution on YOUR website! .
The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle
and smallest angle is $148^\circ$. If the polygon has 3 sides, then find the smallest angle, in degrees.
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As I read the problem, I see that it is about a triangle, whose interior angles form
an arithmetic sequence.
Then I immediately conclude that the central angle of this AP is 60 degrees
(since the sum of the three angles is 180 degrees).
I also conclude that the doubled common difference of the AP is 148 degrees, so
the common difference itself is 148/2 = 74 degrees.
Having it, I immediately conclude that the problem is erroneous: it is self contradictory
and describes a situation which NEVER may happen: it produces the interior angle of this triangle
which has the negative measure of 60-74 = -14 degrees.
Taking everything into account, I conclude that the problem in whole is heavily defective and terminally ill.
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