To find the interior angle \(a\) of the quadrilateral formed by the four angles (given as \(a = 115^\circ\), \(b = 120^\circ\), \(c = 75^\circ\), and \(d = 50^\circ\)), we first need to recall that the sum of the interior angles of a quadrilateral is always \(360^\circ\).
Given that we need to find \(a\) and we already have values for \(b\), \(c\), and \(d\):
\[ b + c + d = 120^\circ + 75^\circ + 50^\circ \]
Calculating this gives:
\[ b + c + d = 120 + 75 + 50 = 245^\circ \]
Now, we can find angle \(a\) by using the formula for the sum of the interior angles of a quadrilateral:
\[ a + b + c + d = 360^\circ \]
Substituting the known values into the equation:
\[ a + 245^\circ = 360^\circ \]
To isolate \(a\), subtract \(245^\circ\) from both sides:
\[ a = 360^\circ - 245^\circ \] \[ a = 115^\circ \]
So, the interior angle measure of \(a\) is:
\[ \text{interior angle a} = 115^\circ \]