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**Alternate Angles**

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**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 are
called alternate interior angles.

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

The alternate angles made by transversal with parallel lines
are always equal and they are also known as ‘z’ shaped angle.

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

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**Alternate exterior angles**

One
pair of angles formed on the opposite side of transversal but outside the two
lines are called alternate exterior angles.

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

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

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*Workout Examples*

*Workout Examples*

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

*Solution: From the figure,*

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

*or, 2x – x = 20° – 10°*

*or, x = 10°*

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

*Solution: From the figure,*

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

*or, 6x – 4x = 50° + 40°*

*or, 2x = 90°*

*or, x = 90°/2*

*or, x = 45°*

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

*Solution: From the figure,*

*a = 50° --------------> Aternate angles.*

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

*or, b + 50° + 70° = 180°*

*or, b + 120° = 180°*

*or, b = 180° – 120°*

*or, b = 60°*

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

*= 50° + 60°*

*= 110°*

*∴*

*a = 50°*

*,*

*b = 60° and c =*

*110°.*

*You can comment your questions or problems regarding lines and angles here.*

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