 ## 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 is external and the other internal are called pair of corresponding angles.
In the given figure above, the pair of corresponding angles are:
i.            ∠AGE and ∠GHD
ii.           ∠AGH and ∠DHF
iii.         ∠EGB and ∠GHC
iv.         ∠BGH and ∠CHF

When two parallel lines are cut by a transversal then the corresponding angles so formed are equal.
In the given figure, MN and PQ are parallel. So, the corresponding angles are equal.
i.            ∠RAM = ∠ABP
ii.           ∠MAB = ∠PBS
iii.         ∠RAN = ∠ABQ
iv.         ∠NAB = ∠QBS

### Workout Examples

Example 1: Find the value of x from the given figure.
Solution: From the figure,
5x – 3° = 3x + 17° -------------> Corresponding angles.
or,     5x – 3x = 17° + 3°
or,     2x = 20°
or,     x = 20°/2
or,     x = 10°

Example 2: Find the value of a and b from the given figure.
Solution: From the figure,
a = 70° -------------> Corresponding angles.
b = a -------------> Corresponding angles.
= 70°

a = 70° and b = 70°

Example 3: Find the value of a, b and c from the given figure.
Solution: From the figure,
a = 50° -------------> Corresponding angles.
b = 70° -------------> Corresponding angles.

c + 50° + 70° = 180° --------> Sum of angles of a Δ.
or,     c + 120° = 180°
or,     c = 180° – 120°
or,     c = 60°

a = 50°, b = 70° and c = 60°

You can comment your questions or problems regarding the corresponding angles and other lines and angles here.