**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.

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.

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.

**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.

**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.

**Solution:**

Here,

From the figure,

a = 50° ------>
Corresponding angles.

b = 70° ------>
Corresponding angles.

Now,

c + 50° + 70° = 180°
------> Sum of angles of a Î”.

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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