In this article, we are going to learn what vertical angles are and how to calculate them. Before we begin, let’s first familiarize ourselves with the following concepts about lines.

You are watching: These are angles opposite one another at the intersection of two lines.

What are intersecting and parallel lines?

Intersecting lines are straight lines that meet or crosses each other at a certain point. The figure below shows the illustration of intersecting lines.

 

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Solution

1400 + z = 1800

z = 1800 – 1400

z = 400

But (x + y) + z = 1800

(x + y) + 400 = 1800

x + y = 1400

900 + y = 1400

y = 500

Example 4

If 1000 and (3x + 7) ° are vertical angles, find the value of x.

Solution

Vertical angles are equal, therefore;

(3x + 7)0 = 100 0

3x = 100 – 7

3x = 93

x = 310

Hence, the value of x is 31 degrees.

Applications of Vertical Angles (h3)

Vertical angles have many applications that we see or experience in our daily lives.

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The roller coasters are being set on a certain angle for proper operation. These angles are so important that if they displaced a degree above or below, there would be a chance of an accident. The maximum vertical angle set for a roller coaster (Mumbo Jumbo, Flamingo Land’s) is 112 degrees.At an airshow, we experience two vapor trails that crosses each other and make vertical angles.Railroad crossing signs (X) placed on the roads for safety of vehicles.A kite, where two wooden sticks crosses and hold the kite.The dartboard has 10 pairs of vertical angles, where the bull’s eye is a virtual vertex.