The sum of the measures of two vertical angles is 300 degrees. Solve for the measures of each angle.
Vertical angles are angles that share the same vertex and are formed by intersecting lines. Vertical angles are always congruent, meaning they have the same measure.
Let's denote the measures of the two vertical angles as x and y. Since the sum of the measures of the two angles is 300 degrees, we can write the equation:
x + y = 300
Since vertical angles are congruent, we know that x = y. Therefore, we can rewrite the equation as:
x + x = 300
2x = 300
x = 150
So, the measure of each angle is 150 degrees.