This statement is never true for convex polygons.
1. Consider the smallest polygon - triangle. As known the sum of measures of interior angles of triangle is 180° (not 250°).
2. The next are quadrilaterals. If you connect two opposite vertices of any quadrilateral, then you get diagonal, which divides the quarilateral into two triangles and the sum of the measures of interior angles of an arbitrary quadrilateral is the sum of the measures of interior angles of these two triangles: 180°+180°=360° (>250°).
3. If you consider pentgons, hexagons and so on, you can noticed then each of these n-sided polygons can be formed by adding triangle to the corresponding (n-1)-sided polygon, then the sum of the measures of interior angles of n-sided polygon is the sum of the measures of interior angles of (n-1)-sided polygon plus 180° (will be greater than 360°). This means that with increasing number of sides, the sum of the measures of the interior angles of a polygon also increases and can never be equal to 250°.
