We’ll most likely learn what vertical angles are and how to calculate them in this brief post. Before we get started, let’s review the following terms and concepts related to lines.

What is the difference between intersecting and parallel lines?

Straight lines that intersect or cross one other at a given point are known as intersecting lines. The image of converging lines is depicted in the diagram below. At factor Q, lines PQ and ST intersect. As a result, the two lines serve as connecting lines. In an airplane, parallel lines are lines that do not meet at any point. Because they do not intersect at any point, lines AB and CD are parallel lines.

Establish Vertical Angles

When two lines intersect, vertical angles are generated as a pair. Angles are sometimes referred to as vertically opposed angles because they are perpendicular to each other. Angles are used in real-world scenarios such as a railway crossing sign, a letter “X,” open scissors pliers, and so on. Egyptians used to draw two intersecting lines and measure the vertical angles to make sure they were equal. The vertical angles remain the same. When two lines converge, we can say that two sets of angles are generated.

Both a and b are vertical opposite angles. The two angles are also identical, i.e. a = c and d form a second set of vertical angles that are likewise equal.

It’s also possible to state that both angles have a same vertex (the specific endpoint of two or more lines or rays).

The Angle Theorem’s Proof We can see in the diagram above that we know angle b and angled are supplementary angles, i.e. We also know that angle a and angled are supplementary angles, i.e. We can rearrange the formulas above: By contrasting the two equations, we arrive at the following conclusion: When two lines converge perpendicularly, extra angles are formed. W and Y, for example, are both angles that are distinct. Similarly, X and Z are two additional vertical angles.

What Is the Best Way to Find Vertical Angles?

Although there is no specific formula for calculating angles, as shown in the examples below, you can identify unknown angles by connecting distinct angles.

Example

In the following number, find the unknown angles.

Solution

The angles 470 and b are vertical. As a result, b has an additional value of 470. (angles are consistent or equal). Supplementary angles are 470 and also. As a result, a = 1800–470 a = 1330 an as well as angles. As a result, c = 1330.

Example

Calculate the value of.

Solution

(+ 20)0 and x are vertical angles in the diagram above. As a result, (+ 20)0 Equals x, whereas 1100 + x = 1800. (auxiliary angles) 700 x = (180– 110)0 In the formula, substitute x = 700; (+ 20)0 = 700 = 700– 200 = 500 As a result, is equal to 50 degrees.