When two lines cross, the angles that are opposite each other are called vertical angles. The two opposing angle pairs are equal to each other. The two adjacent angles are supplementary, which means they sum up to 180 degrees. Complementary angles are defined as two angles that sum up to 90 degrees. There is only one pair of complementary angles in quadrants I and IV - 30 degrees and 150 degrees. In quadrant II there are no complementary angles.

All else being equal, yes, vertical pairs are complementary.

A straight line segment is said to be orthogonal to another straight line segment when their respective vectors (the lines themselves) are perpendicular to each other. All four types of angles are found within orthogonal pairs: two angles between 0 and 90 degrees, two angles between **90 and 180 degrees**, and two angles between **0 and 180 degrees**. These eight combinations of angles always add **up to 360 degrees**. When two angles within **an orthogonal pair** are different, they form a horizontal or a vertical pair.

For example, the angles between the x-axis and the positive side of the y-axis are 45 degrees while those between the y-axis and the negative side of the x-axis are 225 degrees. They form a vertical pair because they add up to 270 degrees instead of 360 degrees. There are no horizontal pairs because all four angles are different.

- Are vertical pairs complementary?
- What is the vertical opposite angle?
- Is a vertical angle complementary or supplementary?
- Are vertical pairs supplementary?
- Why are vertical angles always equal?
- How are vertical adjacent complementary and supplementary relations related?
- What does a vertically opposite angle look like?

What exactly are **vertical angles**? When two lines cross, they generate a pair of vertical angles. Because the angles are opposite each other, vertical angles are frequently referred to as "vertically opposite angles."

There are three types of vertical angles: upper, lower, and central. In mathematics diagrams, these angles are often labeled with the names of their corresponding intersections of lines on the diagram. For example, on the diagram below, the upper vertical angle is called "diagonal" because it is formed by the line labeled "diagonals" and the vertical line labeled "opposite". The lower vertical angle is called "hypotenuse" because it is composed of the horizontal line labeled "hypotenuse" and the vertical line labeled "opposite".

The third type of **vertical angle** is called **the central vertical angle** or median vertical angle. This term comes from the fact that it is in the middle of the diagonal and hypotenuse. The central vertical angle is used when you need to measure a point that is in the exact center of two intersecting lines, such as when measuring a circle's radius. There are two ways to identify the central vertical angle on a diagram: It is the only vertical angle that contains both a diagonal and a hypotenuse. It is also the only vertical angle that is equal to half of another angle.

Vertical angles are diametrically opposed. Congruent vertical angles (equal). The total of the additional angles is 180o. Complementary angles total 90 degrees. Supplementary angles total **more than 180 degrees**.

When two lines connect perpendicularly, vertical angles are formed. W and Y, for example, are vertical angles that are also supplementary angles. When two angles are supplementary, they share **one side** of their intersection. In this case, the shared side is a right angle.

The Egyptians used to draw **two crossing lines** and measure the vertical angles to ensure that they were both equal. This is why vertical angles are always equal.

Summary of the Lesson You discovered that complementary angles are two angles that add up to 90 degrees, supplementary angles are two angles that add **up to 180 degrees**, vertical angles are opposing angles at the junction of two straight lines, and adjacent angles are two angles that are adjacent to each other. These are the only six relationships between angles.

Complementary angles are opposite angles on a circle or in a triangle. If one angle is 90 degrees and the other angle is also 90 degrees, then they are called "complementary" angles because they complete the whole picture - they sum to **180 degrees**. Angles that aren't complementary can be divided into three groups: (1) Vertical angles are opposite angles on a line segment where both angles measure less than 90 degrees. (2) Horizontal angles are opposite angles on a line segment where both angles measure greater than 90 degrees. (3) Oblique angles are opposite angles on a line segment where one angle measures 90 degrees and the other angle measures some other degree value.

If two angles are complementary, their sides are said to be complementary. For example, if an angle measures **45 degrees** and its side is 5 units long, then the two are complementary. If an angle measures 15 degrees and its side is 7 units long, then the two are not complementary because their measurements don't add up to 180 degrees.

When two lines cross, the angles are opposite one other. Adeg and bdeg are vertically opposing angles in **this case**. The term "vertical" refers to the vertex (where they intersect), not up or down.