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Let's represent the two vertical angles as angle A and angle B.
According to the problem, the sum of the measures of the two vertical angles is 300°.
So, we can write the equation as:
A + B = 300
Since vertical angles are congruent, meaning they have the same measure, we can also write the equation as:
A = B
Substituting this into the first equation, we have:
A + A = 300
2A = 300
A = 300/2
A = 150
Therefore, angle A measures 150°.
Since angle A and angle B are congruent, angle B also measures 150°.
So, the measure of each angle is 150°.