NCERT Class 7 Mathematics Solutions: Chapter 5 –Linear and Angles Exercise 5.1 Part 4

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Understanding of Adjacent angles with example

Understanding of Adjacent Angles

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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.