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

Two parallel lines I and m are intersected by a transversal t. If the interior angles on same side of transversal are $(2x-8)^0$ and $(3x-7)^0$ . Find the measure of these angles.
A. 80, 100	B. 70, 110	C. 65, 115	D. 75, 105
Right Option : B
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Question : 2

Are the lines m and l parallel, then the angles shown in the image are:
A. Yes, Corresponding angles	B. Yes, Alternate angles	C. Yes, Co interior angles	D. Not parallel
Right Option : D
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