Question 1166194
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Let the number of sides be " n " (same as the number of vertices).


Then we have for the sum of the interior angles 2*120° + (n-2)*150°.


From the other side, for each n-gon, the sum of its interior angles is (n-2)*180°.


Thus we have this equation

    2*120° + (n-2)*150° = (n-2)*180°.


Simplify it step by step and find n

    2*120 = (n-2)*180 - (n-2)*150

    240   = (n-2)*(180-150)

    240   = (n-2)*30

    n-2 = {{{240/30}}} = 8

    n                  = 8 + 2 = 10.


<U>ANSWER</U>.  n = 10.  The polygon is a decagon (10 sides and 10 vertices).
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Solved.