The sum of the measures of two vertical angles is 300°. Solve for the measure of each angle.
Let's denote the measures of the two vertical angles as x and y.
According to the problem, we know that the sum of the measures of two vertical angles is 300°, which can be written as:
x + y = 300
Since vertical angles are congruent, we can also write the equation:
x = y
Substituting the value of x in terms of y into the first equation, we have:
y + y = 300
Combining like terms, we get:
2y = 300
Dividing both sides of the equation by 2, we find:
y = 150
Thus, the measure of one angle is 150°.
Since the vertical angles are congruent, the measure of the other angle is also 150°.