If the sum of the measurements of two vertical angles is 300 degrees, we can denote the measures of the two angles as \( x \) and \( y \). Since they are vertical angles, they are equal, so we can say:
\[ x + y = 300 \] Since \( x = y \), we can rewrite the equation as:
\[ x + x = 300 \] \[ 2x = 300 \] \[ x = 150 \] Thus, each vertical angle measures 150 degrees.
The answer among the provided options is \( 150 \).