Co Interior Angles


 
 
Concept Explanation
 

Co-Interior Angles

Co-interior angles: The interior angles that lie between two lines and on the same side of a transversal are called co-interior angles. If the two lines are parallel, then co-interior angles add to give small 180^0 and so are supplementary.

In the figure, the following pairs of angles are called pairs of consecutive interior angles: (i)angle 3;and;angle 5;;;;;(ii)angle 4;and;angle 6

Theorem: If the transversal intersects two parallel lines, then each pair of co-interior angles are supplementary.

Given: m and n are parallel lines and the transversal l cuts m and n

To Prove : angle 3 + angle 5=180^0 ;and; angle 4+ angle 6= 180^0

Proof: line m and l intersect each other therefore

angle 3+ angle 4 = 180^0;;;;;...............(1) [ Linear; Pair]   

 Line m and n are parallel and the transversal l cuts them.

angle 4 = angle 5 ;;; .......(2) ;;[ Alternate ;interior;angles;are;equal]

From Eq. (1) and (2)

angle 3 + angle 5 ;= 180^0

Hence Proved that co-interior angles are supplementary.

Theorem: If a transversal intersects two lines such that a pair of co-interior angles are supplementary, then the lines are parallel

Given: m and n are lines and the transversal l cuts m and n and angle 3 + angle 5=180^0

To Prove:  m and n are parallel

Proof: line m and l intersect each other therefore

angle 3+ angle 4 = 180^0;;;;;...............(1) [ Linear; Pair]   

 and

angle 3 + angle 5=180^0 ;;;;........(2) ;;[Given]

From Eq. (1) and (2)

angle 4 = angle 5

But they are alternate interior angles when the transversal l cuts the line m and n

Since they are equal the lines are parallel.

Hence Proved that the lines are parallel.

Illustration: Identify co - interior angles from the given figure:

Solution: <3 and <5 are co - interior <3 + <5 = 180.

<4 and <6 are co - interior and  <4 + <6 = 180. because AB and CD are two parallel lines and a transversal L intersects them:

  • (i) each pair of corresponding angles are equal
  • (ii) each pair of alternate interior angles are equal and,
  • (iii) each pair of consecutive interior angles are supplementary.
  • The converse of each of the above statements is also true.

    Find ;the; value ;of; x ;from ;the ;given; figure :

    Solution: As co-interior angles are supplementary

    5x + 37 + 43 = 180 

    5x =180-80

    5x=100

    x = 20

       
    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Find the value of 8x using definition of co-interior angles from the  following diagram

    Right Option : B
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    Explanation
    Question : 2

    If a transversal intersects two parallel lines then each pair of consecutive interior angles is ________________________.

    Right Option : B
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    Explanation
    Question : 3

    Find the values of both the angles marked in the following figure

    Right Option : B
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    Explanation
     
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