Vertical angles are pairs of angles that are opposite each other when two lines intersect. They are always equal to each other. If the sum of the measures of the two vertical angles is 300°, we can represent each angle as \( x \).
Since they are equal, we have:
\[ x + x = 300° \]
This simplifies to:
\[ 2x = 300° \]
Now, divide both sides by 2:
\[ x = 150° \]
Thus, each vertical angle measures 150°.
The answer is \( 150° \).