# 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.

**☛ Related Questions:**

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