Vertical angles are equal, which means that if the sum of the measures of the two vertical angles is 300 degrees, we can express the angles as \( x \) and \( x \) (since they are equal). Thus, we can set up the following equation:
\[ x + x = 300 \]
This simplifies to:
\[ 2x = 300 \]
Now, divide both sides by 2:
\[ x = 150 \]
Therefore, the measure of each angle is \( 150 \) degrees.
The answer is: A. 150.