In each of the following figures, write, if any, each linear pair
Solution:
We know that
Linear pairs of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
(i) Given, the figure represents two lines intersected by another line at two distinct points.
We have to write each linear pair of angles.
From the figure,
The linear pair of angles are
∠1 and ∠2
∠1 and ∠4
∠3 and ∠4
∠2 and ∠3
∠5 and ∠6
∠5 and ∠8
∠6 and ∠7
∠7 and ∠8
(ii) Given, the figure represents two rays produced from a point B on a line AC.
From the figure,
The linear pair of angles are
∠ABD and ∠DBC
∠ABE and ∠EBC
(iii) Given, the figure represents three lines in the form of letter Z.
From the figure,
We observe that there are no linear pair of angles since two lines do not intersect.
(iv) Given, the figure represents two lines RS and PQ intersecting at O and a ray OT.
From the figure,
The linear pair of angles are
∠ROP and ∠POS
∠ROP and ∠ROQ
∠ROT and ∠SOT
∠SOQ and ∠SOP
∠QOT and ∠POT
∠ROQ and ∠SOQ
Therefore, each pair of vertically opposite angles and each linear pair of each figure is given above.
✦ Try This: Write down each linear pair of angles shown in the following figure:
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 73(ii) - (i), (ii), (iii), (iv)
In each of the following figures, write, if any, each linear pair
Summary:
In each of the following figures, each linear pair are (i) The linear pair of angles are ∠1 and ∠2, ∠1 and ∠4, ∠3 and ∠4, ∠2 and ∠3, ∠5 and ∠6, ∠5 and ∠8, ∠6 and ∠7, ∠7 and ∠8, (ii) The linear pair of angles are ∠ABD and ∠DBC, ∠ABE and ∠EBC, (iii) No linear pair of angles, (iv) The linear pair of angles are ∠ROP and ∠POS, ∠ROP and ∠ROQ, ∠ROT and ∠SOT, ∠SOQ and ∠SOP, ∠QOT and ∠POT, ∠ROQ and ∠SOQ
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