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

Answer 1

Vertical angles are pairs of angles that are opposite each other when two lines intersect. One important property of vertical angles is that they are always equal in measure.

Let's denote the measure of one of the vertical angles as $x$. Since the two angles are vertical angles, the measure of the other angle will also be $x$.

According to the problem, the sum of the measures of the two vertical angles is 300°:

$$x+x=300°$$

This simplifies to:

$$2x=300°$$

To find $x$, divide both sides by 2:

$$x=\frac{300°}{2}=150°$$

Thus, both vertical angles measure $150°$.

Therefore, the measure of each angle is $150°$.