Before jumping right into the topic of equivalent angles, let’s very first remind ourselves about angles, parallel and non-parallel lines, and also transversal lines.

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In Geometry, an edge is composed of three parts: vertex and also two arms or sides. The vertex of an angle is where 2 sides or currently of the edge meet, while arms of an angle are just the angle’s sides.

Parallel lines room two or much more lines on a 2-D plane that never meet or cross. ~ above the various other hand, non-parallel lines space two or more lines that intersect. A transversal line is a heat that crosses or passes with two other lines. A transverse line deserve to pass through two parallel or non-parallel lines.

## What is a equivalent Angle?

Angles formed when a transversal heat cuts across two right lines are well-known as corresponding angles. Corresponding angles are situated in the same loved one position, an intersection that transversal and also two or much more straight lines.

The angle rule of corresponding angles or the corresponding angles postulates that the matching angles are equal if a transversal cuts two parallel lines.

Corresponding angles space equal if the transversal line crosses at the very least two parallel lines.

The diagram listed below illustrates corresponding angles formed when a transversal line crosses 2 parallel lines:

Solution

Given the ∠d = 30°

d = ∠b (Vertically the contrary angles)

Therefore, ∠b = 30°

b = ∠ g= 30° (corresponding angles)Now, ∠ d = ∠ f (Corresponding angles)

Therefore, ∠f = 30°∠ b + ∠ a = 180° (supplementary angles)

a+ 30° = 180°

a = 150°

a = e = (corresponding angles)

Therefore, ∠e = 150°

d = h = 30° (corresponding angles)

Example 2

The two equivalent angles of a number measure 9x + 10 and also 55. Find the value of x.

Solution

The two equivalent angles are always congruent.

Hence,

9x + 10 = 55

9x = 55 – 10

9x = 45

x = 5

Example 3

The two corresponding angles the a figure measure 7y – 12 and also 5y + 6. Uncover the magnitude of a corresponding angle.

Solution

First, we need to identify the worth of y.

The two equivalent angles are constantly congruent.

Hence,

7y – 12 = 5y + 6

7y – 5y = 12 + 6

2y = 18

y = 9

The magnitude of a corresponding angle,

5y + 6 = 5 (9) + 6 = 51

### Applications of equivalent Angles

There exist plenty of applications of equivalent angles which us ignore. Observe them if you ever get a chance.

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Usually, windows have horizontal and vertical grills, which do multiple squares. Every vertex of the square provides the matching angles.The bridge stands on the pillars. Every pillars are connected in together a method that equivalent angles are equal.The railway tracks room designed so that all the corresponding angles space equal top top the track.