Question 1107580
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<pre>
You can express the sum of all interior angle of any convex polygon with n sides (n vetices) as 180°*(n-2).


From the other side, the sum of all interior angle of any regular polygon is {{{n*alpha)}}}, where {{{alpha}}} is any of its interioir angle.


Thus you have this equation

180*(n-2) = n*156.


where n is unknown number of sides (of vertices).  Simplify and solve for n:


180n - 360 = 156n  ====>  180n - 156n = 360  ====>  24n = 360  ====>  n = {{{360/24}}} = 15.


<U>Answer</U>.  15 sides  and/or  15 verices.
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Solved.