Alternate Angles

Alternate Angles


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.


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.


'Z' shaped angles (alternate angles)

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.


Alternate exterior angles

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.


Example 1: Find the value of x.

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.


Example 2: Find the value of x.

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.


Example 3: Find the value of a, b and c.

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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