NCERT Solutions for Class 7 Maths Chapter 5 - Lines and Angles Exercise 5.1

Refer to page 3-6 for Exercise 5.1 in the PDF.

1. Find the complement of each of the following angles.

(i)

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $20^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then,

$ = x + 20^\circ  = 90^\circ $

$ = x = 90^\circ  - 20^\circ $

$ = x = 70^\circ $

Hence, the complement of the given angle measures $70^\circ $.

(ii) 

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $63^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then,

$ = x + 63^\circ  = 90^\circ $

$ = x = 90^\circ  - 63^\circ $

$ = x = 27^\circ $

Hence, the complement of the given angle measures $27^\circ $.

(iii)

Ans: Here, two angles are said to be complementary if the sum of their measures is $90^\circ $.

As the given angle is $57^\circ $.

Now, let the measure of its complement be $x^\circ $.

Then, 

$ = x + 57^\circ  = 90^\circ $

$ = x = 90^\circ  - 57^\circ $

$ = x = 33^\circ $

Hence, the complement of the given angle measures $33^\circ $.

2. Find the supplement of each of the following angles:

i) 

Ans: Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $105^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 105^\circ  = 180^\circ $

$ = x = 180^\circ  - 105^\circ $

$ = x = 75^\circ $

Hence, the  supplement of the given angle measures $75^\circ $

ii) 

Ans: Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $87^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 87^\circ  = 180^\circ $

$ = x = 180^\circ  - 87^\circ $

$ = x = 93^\circ $

Hence, the  supplement of the given angle measures $93^\circ $

iii) 

Here, two angles are said to be supplementary if the sum of their measures is $180^\circ $.

As the given angle is $154^\circ $.

Now, let the measure of its  supplement be $x^\circ $.

Then, 

$ = x + 154^\circ  = 180^\circ $

$ = x = 180^\circ  - 154^\circ $

$ = x = 26^\circ $

Hence, the  supplement of the given angle measures $26^\circ $

3. Identify which of the following pairs of angles are complementary and which are supplementary.

i) $65^\circ ,115^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 65^\circ  + 115^\circ $

$ = 180^\circ $

If the sum of two angle measures is $180^\circ $, then the two angles are said to be supplementary.

Therefore, these angles are supplementary angles.

ii) $63^\circ ,27^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 63^\circ  + 27^\circ $

$ = 90^\circ $

If the sum of two angle measures is $90^\circ $, then the two angles are said to be complementary.

Therefore, these angles are complementary angles.

iii) $112^\circ ,68^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 112^\circ  + 68^\circ $

$ = 180^\circ $

If the sum of two angle measures is $180^\circ $, then the two angles are said to be supplementary.

Therefore, these angles are supplementary angles.

iv) $130^\circ ,50^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 130^\circ  + 50^\circ $

$ = 180^\circ $

If the sum of two angle measures is $180^\circ $, then the two angles are said to be supplementary.

Therefore, these angles are supplementary angles.

v) $45^\circ ,45^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 45^\circ  + 45^\circ $

$ = 90^\circ $

If the sum of two angle measures is $90^\circ $, then the two angles are said to be complementary.

Therefore, these angles are complementary angles.

vi) $80^\circ ,10^\circ $

Ans: Here, we have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

$ = 80^\circ  + 10^\circ $

$ = 90^\circ $

If the sum of two angle measures is $90^\circ $, then the two angles are said to be complementary.

Therefore, these angles are complementary angles.

4. Find the angles which is equal to its complement.

Ans: Firstly, let the measure of the required angle be $x^\circ $

As we know that, the sum of measures of complementary angle Pair is $90^\circ $.

Then,

$ = x + x = 90^\circ $

$ = 2x = 90^\circ $

$ = x = \frac{{90}}{2}$

$ = x = 45^\circ $

Hence, the required angle measure is $45^\circ $.

5. Find the angles which is equal to its supplement.

Ans: Firstly, let the measure of the required angle be $x^\circ $

As we know that, the sum of measures of supplementary angle Pair is $180^\circ $.

Then,

$ = x + x = 180^\circ $

$ = 2x = 180^\circ $

$ = x = \frac{{180}}{2}$

$ = x = 90^\circ $

Hence, the required angle measures is $90^\circ $.

6. In the given figure,$\angle 1$ and $\angle 2$are supplementary angles. If $\angle 1$is decreased, what changes should take place in $\angle 2$so that both angles still remain supplementary.

Ans: In the question, it is given that,

$\angle 1$and$\angle 2$are both supplementary angles.

If $\angle 1$is decreased, then $\angle 2$ must be increased by the same value. Hence, this angle pair remains supplementary.

7. Can two angles be supplementary if both of them are :

i) Acute?

Ans: No. If two angles are acute, it means less than $90^\circ $, the two angles cannot be supplementary.  Because, their sum will be always less than $90^\circ $.

ii) Obtuse?

Ans: No. If two angles are obtuse, it means more than $90^\circ $, the two angles cannot be supplementary.  Because, their sum will always be more than $90^\circ $.

iii) Right?

Ans: Yes. If two angles are right, it means both measures$90^\circ $, the two angles can form a supplementary pair.  Because, their sum will be equal to$90^\circ $.

$\therefore 90^\circ  + 90^\circ  = 180^\circ $.

8. An angle is greater than $45^\circ $. Is it complementary angle greater than $45^\circ $or equal to $45^\circ $or less than $45^\circ $ ?

Ans: Here, let us assume that the complementary angles be p and q.

As we know, the sum of measures of complementary angle pairs is $90^\circ $.

Then,

$ = p + q = 90^\circ $

It is given in the question that angle $p > 45^\circ $.

Now, adding q on both the sides, 

$ = p + q > 45^\circ  + q$

$ = 90^\circ  > 45^\circ  + q$

$ = 90^\circ  - 45^\circ  > q$

$ = q < 45^\circ $

Hence, its complementary angle is less than $45^\circ $.

9. Fill in the blanks :

i) If two angles are complementary, then the sum of their measures is __________ .

Ans: $90^\circ$

ii) If two angles are supplementary, then the sum of their measures is __________.

Ans: $180^\circ$

iii) If two adjacent angles are supplementary, they form a ______.

Ans: Linear pair

10. In the adjoining figure, name of the following pairs of angles.

i) Obtuse vertically opposite angles

Ans: $\angle AOD$ and $\angle BOC$ are obtuse vertically opposite angles in the given figure.

ii) Adjacent complementary angles

Ans: $\angle EOA$ and $\angle AOB$ are adjacent complementary angles in the given figure.

iii) Equal supplementary

Ans: $\angle EOB$ and $\angle EOD$ are equal supplementary angles in the given figure.

iv) Unequal supplementary angles

Ans: $\angle EOA$ and $\angle EOC$ are unequal supplementary angles in the given figure.

v) Adjacent angles that do not form a linear pair.

Ans: $\angle AOB$ and $\angle AOE$, $\angle AOE$ and $\angle EOD$ , $\angle EOD$ and $\angle COD$ are the adjacent angles that do not form a linear pair in the given figure.

Conclusion

Class 7 Maths Ex 5.1 is vital for building a strong foundation in geometry. It focuses on the fundamental properties of lines and angles, including parallel and perpendicular lines, and acute, obtuse, and right angles. Understanding these basics is essential for solving more complex problems in future chapters. Pay close attention to the definitions and properties, as they are crucial for grasping the concepts. Vedantu’s detailed solutions will guide you through these topics, ensuring you develop a solid understanding and excel in your studies.

Class 7 Maths Chapter 5: Exercises Breakdown

CBSE Class 7 Maths Chapter 5 Other Study Materials

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