 ## 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 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.

### 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.

### 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°.

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