**Alternate Angles**

**Alternate interior
angles**

When two lines are cut by a transversal then the pair of angles
on the opposite sides of the transversal but inside the two lines (i.e.
interior angles) are called **alternate interior angles**.

In the given figure ∠c and ∠f, ∠d and ∠e are pairs of alternate angles.

The alternate angles made by a transversal with parallel lines are always equal and are also known as ‘Z’ shaped angles as shown in the figure given below.

In the figure, ∠a = ∠b as they are alternate (‘Z’ shaped) angles made by the transversal
with parallel lines.

**Alternate exterior
angles**

Pair of angles formed on the opposite side of transversal but
outside the two lines (i.e. exterior angles) are called **alternate exterior
angles**.

Alternate exterior angles are equal if two parallel lines are cut by a transversal line.

In the figure given above, RS is parallel to PQ and EF is a transversal,
therefore the alternate exterior angles are equal. i.e. ∠a = ∠c and ∠b = ∠d.

**Worked Out Examples**

**Example 1:** Find the value of x from the given figure.

**Solution:**

Here,

From the figure,

2x + 10° = x + 20° ------>
Aternate angles are equal.

or, 2x – x = 20° – 10°

or, x = 10° Ans.

**Example 2:** Find the value of x from the given figure.

**Solution: **

Here,

From the figure,

6x – 40° = 4x + 50° ------>
Aternate exterior angles are equal.

or, 6x – 4x = 50° + 40°

or, 2x = 90°

or, x = 90°/2

or, x = 45° Ans.

**Example 3:** Find the value of a, b, and c from the given figure.

**Solution: **

Here,

From the figure,

a = 50° ------>
Alternate angles.

Now,

b + a + 70° = 180° ------>
Straight angle.

or, b + 50° + 70° = 180°

or, b + 120° = 180°

or, b = 180° – 120°

or, b = 60°

Again,

c = a + b ------>
Alternate angles.

= 50° + 60°

= 110°

If you have any questions or problems regarding the **Alternate Angles**, you can ask here, in the comment section below.

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