Examples of Corresponding Angles

Example 1: If two corresponding angles formed by parallel lines are 2x + 1 and 87. Find the value of x.

Solution:

Given 2x + 1 and 87 are corresponding angles formed by parallel lines hence they are equal to each other.

Therefore, 2x + 1 = 87

=> 2x = 87-1

=> 2x = 86

=> x = 86/2

=> x = 43

Hence the value of x is 43.

Example 2: For y = 1, Check whether 3y – 1 and 5 + y are corresponding to each other or not.

Solution:

For y = 1,

Value of 3y – 1

= 3 × 1 – 1

= 3 -1 = 2

and the value of 5 + y

= 5 + 1 = 6

Hence, 3y – 1 ≠ 5 + y

The values of the given two angles are not the same hence these corresponding angles are not formed by parallel lines.

Example 3: For two parallel lines, Find the value of x if 7x – 4 and 2x + 6 are corresponding to each other. Also, find the value of each corresponding angle.

Solution:

Given 7x – 4 and 2x + 6 are corresponding angles formed by parallel lines hence they are equal to each other.

Therefore, 7x – 4 = 2x + 6

Solving the above equation we get,

7x – 4 = 2x + 6

=> 7x – 2x = 6 + 4

=> 5x = 10

=> x = 10/5

=> x = 2

Put x = 2 in 7x – 4 we get

= 7 × 2 – 4

= 14 -4

= 10

Hence the value of x is 2 and the measure of each corresponding angle is 10° .

Example 4: If 5z and 2z + 12 are corresponding angles. For z = 4, check if the lines forming these corresponding angles are parallel or not.

Solution:

For z = 4

Value of 5z = 5 × 4 = 20

and value of 2z + 12 = 2 × 4 + 12 = 8 + 12 = 20

Hence, for z=4, the value of 5z = 2z + 12 and so the given corresponding angles are formed by parallel lines.

Corresponding Angles are the relative angles formed on the corresponding corners when a transversal line intersects two other lines. Corresponding angles have important applications in the field of mathematics and physics. It helps to solve geometry problems, like finding unknown angles or determining congruent angles and figures. The real-life example based on the use of corresponding angles can be seen in railway tracks and Rubik’s cube.

In this article, we will learn about the corresponding angle, along with its definition, theorems, and some examples for better understanding.