Question 1183295
.
<pre>
Let "n" be the number of sides of the polygon (the same as the number of vertices).


Two interior angles are 120 degrees each, and the other (the rest) (n-2) interior angles are 150 degrees each.


Write equation for the sum of all interior angles


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


Simplify and find "n"


    240 + 150n - 300 = 180n - 360

    240 + 360  - 300 = 180n - 150n

          300        = 30n

            n        = 300/30 = 10.


Thus the polygon has 10 sides and 10 vertices.


The sum of the interior angles is  (10-2)*180 = 8*180 = 1440 degrees.     <U>ANSWER</U>
</pre>

Solved.