Corresponding Angles

Corresponding Angles

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. 
two lines AB and CD has been cut by a transversal EF at G and H
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. 
MN//PQ has been cut by a transversal RS at A and B
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.
Example 1: Find the value of x.
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.
Example 2: Find the value of a and b.
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.
Example 3: Find the value of a, b and c.
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.

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