Question - Calculating the Sum of Interior Angles in a Polygon

Let n be the number of sides (or angles) in the polygon.

The formula for the sum of the interior angles in an n-sided polygon is:

\[ (n - 2) \times 180^\circ \]

We are given that one angle measures \( 50^\circ \). As the polygon appears to be a rhombus, all angles are equal.

Since there are four angles in total, we can write:

\[ 4 \times 50^\circ = (n - 2) \times 180^\circ \]

\[ 200^\circ = (n - 2) \times 180^\circ \]

The exact question being asked is not clear from the image, but assuming we need to confirm if the angles provided can form a polygon, we can solve for n:

\[ n - 2 = \frac{200^\circ}{180^\circ} \]

\[ n - 2 = \frac{20}{18} \]

\[ n - 2 = 1\frac{1}{9} \]

Given that n must be a whole number, the answer 1\(\frac{1}{9}\) indicates that the values presented do not form a consistent set for a polygon with all equal angle measures. Hence, there seems to be a discrepancy unless the intention was to showcase an irregular polygon, in which case additional information would be needed.