Question

In which diagram do angles 1 and 2 form a linear pair?

2 lines intersect and form 4 angles. Labeled clockwise from the top: blank, 2, blank, 1.
3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.
A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.
A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

Answer 1

the correct answer for this question is option 1

Answer 2

Given :   4 Diagrams

Fig 1 : 2 lines intersect and form 4 angles. opposite angles 1 & 2

Fig 2 : 3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.

Fig 3 : A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.

Fig 4 :   A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

To find :  In which diagram do angles 1 and 2 form a linear pair?

Solution:

Fig 1   :  Vertically opposite angles are equal

∠1 = ∠2

Hence it does not form a linear pair

Fig 2 : 3 lines extend from a point and form 2 angles, labeled 1 and 2. Both angles add up to 90 degrees.

Hence it does not form a linear pair

Fig 3 : A horizontal line has 2 lines extending from a midpoint forming 3 angles. Labeled from left to right: 1, 2, 3.

∠1 + ∠2 + ∠3 = 180°

=> ∠1 + ∠2  =  180° - ∠3  

Hence it does not form a linear pair

Fig 4 :  A horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

∠1 + ∠2  =  180° ( straight line)

in Fig 4   angles 1 and 2 form a linear pair

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