Linear Pair


 
 
Concept Explanation
 

LINEAR PAIR

It is a pair of adjacent angles in which the non common arms form a Straight Lines.

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.

Illustration:  Find the values of the angles x, y and z in each of the following:

Solution:  large 80^{circ}+x+30^{circ}=180^{circ}    [Angles on a straight line]

110 + x = 180 :   x = 180 - 110 = 70 

large 80^{circ}+y=180^{circ}     [Linear pair]

y = 180 - 80 = 100      (i)

Also  Y + Z = 180    [Linear pair]

100 + Z = 180 : Z = 180 - 100 = 80         

                             

Illustration: Find the value of x if it forms a linear pair with angle whose measure is 118 degrees.

Solution: As x and angle 118 degrees forms a pair of linear angle. Hence we must have

large x^{0}+118^{0}=180^{0}

large therefore x^{0}=180^{0}-118^{0}

large therefore x=62^{0}

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

In the given figure, two straight lines PQ and RS intersect each other at O. If angle POT=75^{0} ,then   the value of 'b' is   __________________

Right Option : D
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Explanation
Question : 2

If the given angles form a linear pair of angles,find the value of x.

Right Option : B
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Explanation
Question : 3

In the given figure, AOC is a line. Find the value of   frac{x}{5} .

Right Option : C
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Explanation
 
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