In (Fig 5.42) are the following pairs of angles adjacent? Justify your answer
Solution:
We have to determine which figure represents a pair of adjacent angles.
Adjacent angles are the angles that have a common arm (side) and a common vertex, however, they do not overlap.
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
From the properties of adjacent angles, we know that
a. Adjacent angles always share a common arm.
b. They have a non-common arm on both sides of the common arm.
Considering figure (i),
We observe that a and b have a common vertex and common arm.
a and b do not overlap
Therefore, the figure (i) represents a pair of adjacent angles.
Considering figure (ii),
a and b have a common vertex but no common arm.
Therefore, figure (ii) does not represent a pair of adjacent angles.
Considering figure (iii),
a and b do not have common vertex and common arm
Therefore, figure (iii) does not represent a pair of adjacent angles.
Considering figure (iv),
We observe that a and b overlap
Therefore, figure (iv) does not represent a pair of adjacent angles.
✦ Try This: Find the supplement of the angle 70°.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 82
In (Fig 5.42) are the following pairs of angles adjacent? Justify your answer
Summary:
In Fig 5.42, the figure (i) represents a pair of adjacent angles. They have a common vertex and a common arm and do not overlap.
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