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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 =
= 8
n = 8 + 2 = 10.
ANSWER. n = 10. The polygon is a decagon (10 sides and 10 vertices).
Solved.