NCERT Class 7 Mathematics Solutions: Chapter 5 – Linear and Angles Exercise 5.1 Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Understanding of Adjacent Angles with Example

1. An angle is greater than . Is its complementary angle greater than or equal to or less than ?

Answer:

Consider are two angles making a complementary angle pair and is greater than .

So, will be lesser than .

2. In the adjoining figure:

(i) Is adjacent to ?

(ii) Is adjacent to ?

(iii) Do form a linear pair?

(iv) Are supplementary?

(v) Is vertically opposite to ?

(vi) What is the vertically opposite angle of ?

Given Adjoin Point

Answer:

(i) Yes. Since they have a common vertex and also a common arm .

Also, their non-common arms, , are on either side of the common arm.

(ii) No. They have a common vertex and also a common arm .

However, their non-common arms, , are on the same side of the common arm.

So, these are not adjacent to each other.

(iii) Yes. Since they have a common vertex and a common arm .

Also, their non-common arms, , are opposite rays.

(iv) Yes. Since have a common vertex and their non-common arms are opposite to each other.

(v) Yes. Since these are formed due to the intersection of two straight lines () .

(vi) is the vertically opposite angle of as these are formed due to the intersection of two straight lines, .

4. Indicate which pairs of angles are:

(i) Vertically opposite angles.

(ii) Linear pairs.

Given Vertically Opposite Angles and Linear Pairs

Answer:

(i) are vertically opposite angles as these are formed due to the intersection of two straight lines.

(ii) as these have a common vertex and also have non-common arms opposite to each other.