![Corresponding Angles Corresponding Angles](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMjoyvevRhwQlfCrZOqFFt8iYXBVjy1KxiyUGI5rOguf6ZU8jv09RQWWYx4MizhNi9ZGLf6NWBD4wZysLVlLQJrEMCz5dd5A8EPxcFCMNI7-bRNok9h1ogBpJjV3f_VuVhdJNCDWZAZNmD/s16000/corresponding+angles.png)
Corresponding Angles
When two lines are cut by a transversal, then a pair of non-adjacent angles on the same side of a transversal, one external and the other internal are called corresponding angles.
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In the figure given below, transversal EF has been cut to the two non-parallel lines AB and CD at G and H.
![Corresponding angles in non-parallel lines. Two lines AB and CD has been cut by a transversal EF at G and H](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrPyyQfGxUNJg_gJERNEBdEayIe4jJ5ftXH3z5kQp8oOIzfQoF-idxc8NFFHA984HpLt1JX1TEaSA2EvKU9wGBSA5OX-ICuLgMycfMl0Sm0c4juV6Wh13M3JWHA4FBiORdNzs7vso5Ctlq/s16000/corresponding+angles+non+parallel.png)
Here, the corresponding angles are:
i.
∠AGE and ∠GHD
ii.
∠AGH and ∠DHF
iii.
∠EGB and ∠GHC
iv. ∠BGH and ∠CHF
If two parallel lines are cut by a transversal then the corresponding angles are equal. In below figure, transversal RS has been cut to the two parallel lines MN and PQ at A and B.
![Corresponding angles in parallel lines Two parallel lines AB and CD has been cut by a transversal EF at G and H](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdz4HaS03dF59npCOjGGqEgq2s7fgnAe7z9p8KeyEExJe5cc44O1z0rNCcQjkCOBU6w51hvbD23vx6Iboq0eojhVQDhcFCYCW7MEJaHIQ7GSPjALnroBPKfQeGElMd9TLophxNynUibNu9/s16000/corresponding+angles+parallel+lines.png)
So, the
corresponding angles are equal. i.e.
i.
∠RAM = ∠ABP
ii.
∠MAB = ∠PBS
iii.
∠RAN = ∠ABQ
iv.
∠NAB = ∠QBS
Worked Out Examples
Example 1: Find the value of x from the given figure.
![Example 1: Find the value of x.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEgDK93ogg38Ra4cqYI-v0utQ_5EtVdH97biDsEIbK0Fomv5f7qmsYbftogwifPOXmHX-oNBFLv9qNO7TfpD8qRPd_P2KWH_0VQEQD2L9y56jniXGndfjoj4y4Fs5LpyoXbSsrEx9-Bsii/s16000/example+1.png)
Solution:
Here,
From the figure,
5x – 3° = 3x + 17°
------> Corresponding angles.
or, 5x – 3x = 17° + 3°
or, 2x = 20°
or, x = 20°/2
or, x = 10° Ans.
Example 2: Find the value of a and b from the given figure.
![Example 2: Find the value of a and b. Example 2: Find the value of a and b.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqFmu32uVfByMcTpYSgxH__-DN7de-a15bpAWkvhwSgsOSdJsI1LkMLVpkJ_DlbKhWMNcLq2vYFv1TR31504KJBktaSXnmfAa_yfAF3QWqk0OZCsatdI_tjjse-Q9a3XIusJtEyIkH9mGh/s16000/example+2.png)
Solution:
Here,
From the figure,
a = 70° ------>
Corresponding angles.
b = a ------>
Corresponding angles.
= 70°
∴ a = 70° and b = 70° Ans.
Example 3: Find the value of a, b and c from the given figure.
![Example 3: Find the value of a, b and c. Example 3: Find the value of a, b and c.](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge7SLVYlmF_Y1oNzTvMgjUf4DJsR9In2MaEyn8bf3jA5zTc7Lgjm8MlLEdiUtuS29fmtjNs6mxEUA81g2p8Y2ThQvI5QEftrXgdiZKiZ83w1HwMoiJ_si3UdXxAkq5r_pfzn1fkUI-8opi/s16000/example+3.png)
Solution:
Here,
From the figure,
a = 50° ------>
Corresponding angles.
b = 70° ------>
Corresponding angles.
Now,
c + 50° + 70° = 180°
------> Sum of angles of a Δ.
or, c + 120° = 180°
or, c = 180° – 120°
or, c = 60°
∴ a = 50°, b = 70° and c = 60° Ans.
If you have any questions or problems regarding the Corresponding Angles, you can ask here, in the comment section below.
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