##
**Transversal**

In geometry, a transversal is a line which cuts two or more
lines at distinct points. In the figure given below, lines AB and CD are cut by
the line EF at the points G and H respectively. So, EF is a transversal.

###
**Types of angles formed by a
transversal**

When two line segments are cut by a transversal then there
will form 8 angles. In the figure given above, transversal EF has cut the line
segments AB and CD at points G and H respectively. The angles formed there are ∠AGE, ∠BGE, ∠AGH, ∠BGH, ∠GHC, ∠GHD, ∠CHF and ∠DHF.

**The angles formed inside the two line segments are called interior angles. In the given figure, angles ∠AGH, ∠BGH, ∠GHC and ∠GHD are interior angles.**

__Interior angles__:**The angles formed outside the two line segments are called exterior angles. In the given figure, angles ∠AGE, ∠BGE, ∠CHF and ∠DHF are exterior angles.**

__Exterior angles__:####
**Alternate angles**

A pair of non adjacent interior angles on the opposite sides
of a transversal is called alternate angles.

In the figure the alternate angles
are:

i. ∠AGH and ∠GHD

ii. ∠BGH and ∠GHC

**Note:**When the two lines cut by transversal are parallel, then alternate angles are equal.####
**Corresponding angles**

In a pair of non-adjacent angles on the same side of a
transversal, one is external and other internal are called corresponding
angles.

In the figure the corresponding angles are:

i. ∠AGE and ∠GHC

ii. ∠AGH and ∠CHF

iii. ∠BGE and ∠GHD

iv. ∠BGH and ∠DHF

**Note:**When the two lines cut by transversal are parallel, then corresponding angles are equal.####
**Co-interior angles**

A pair of two interior angles on the same side of a
transversal are called co-interior angles.

In the figure the co-interior angles
are:

i. ∠AGH and ∠GHC

ii. ∠BGH and ∠GHD

**Note:**When the two lines cut by transversal are parallel, then co-interior angles are supplementary i.e. their sum is 180°.###
*Workout Examples*

*Workout Examples*

*Example 1: Find the values of a, b, c and d from the given figure.*

*Solution: Here,*

*5a + 30° + 3a – 10° = 180° ----------------> sum of co-interior angles*

*or, 8a + 20° = 180°*

*or, 8a = 180° - 20°*

*or, a = 160°/8*

*or, a = 20°*

*b = 5a + 30° --------------------> Corresponding angles*

*= 5×20° + 30°*

*= 100° + 30°*

*= 130°*

*c = 3a – 10° --------------------> Alternate angles*

*= 3×20° – 10°*

*= 60° – 10°*

*= 50°*

*d = c ----------------------> Vertically opposite angles*

*= 50°*

*∴*

*a = 20°, b = 130°, c = 50° and d = 50°*

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