The sum of the measures of two vertical angles is 300°. Solve for the measure of each angle.

Answer 1

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°.