18. Two lines intersect at a point. the vertical angles formed are supplementary. What is the measure of each of the angles? Explain.

since vertical angles are equal, and supplementary angles add to 180, if the vertical angles have measure x, then

x+x = 180

When two lines intersect, they form four angles at the point of intersection. The vertical angles are a pair of opposite angles formed by the intersection of these lines.

Vertical angles are always congruent, meaning they have the same measure. Additionally, when two angles are supplementary, their measures add up to 180 degrees.

Therefore, if the vertical angles are supplementary, each angle must measure half of 180 degrees, which is 90 degrees. Thus, the measure of each vertical angle formed by the lines intersecting is 90 degrees.

To find the measure of each angle, let's start by understanding what vertical angles are.

When two lines intersect, four angles are formed at the intersection point. Vertical angles are the opposite angles formed by the intersecting lines. They are congruent to each other, meaning they have the same measure.

Now, we are given that the vertical angles are supplementary. Supplementary angles are two angles whose sum is 180 degrees. So, if the vertical angles are supplementary, their sum is 180 degrees.

Let's represent the vertical angles as angles A and B. Since they are congruent, we can say that angle A = angle B = x (where x represents the measure of each angle).

Since the vertical angles are supplementary, we can set up the equation:

angle A + angle B = 180 degrees

Substituting the measure of each angle (x) into the equation:

x + x = 180 degrees

Simplifying the equation:

2x = 180 degrees

Now, we need to solve for x by dividing both sides of the equation by 2:

2x/2 = 180 degrees/2

x = 90 degrees

Therefore, the measure of each of the vertical angles is 90 degrees.