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

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. In the adjoining figure:

i) Is  $\angle 1$adjacent to $\angle 2$?

Ans: After observing the figure we can understand that,

Yes, as $\angle 1$and $\angle 2$ having a common vertex i.e., O a common arm OC.

Their non-common arms OA and OE are on both sides of the common arm.

ii) Is $\angle AOC$adjacent to $\angle AOE$?

Ans: After observing the figure we can understand that,

No, they are having a common vertex i.e., O a common arm OA.

But , they have non- non-common arms on both sides of the common arm.

iii) Do $\angle COE$ and $\angle EOD$ form a linear pair?

Ans: After observing the figure we can understand that,

Yes, as $\angle COE$and $\angle EOD$ have a common vertex i.e., O a common arm OE. 

Their non-common arms OC and OD are on both sides of the common arm.

iv) Are $\angle BOD$ and$\angle DOA$supplementary?

Ans: After observing the figure we can understand that,

Yes, as $\angle BOD$and$\angle DOA$  having a common vertex i.e., O a common arm OE. 

Their non-common arms OA and OB are on both sides of the common arm.

v) Is $\angle 1$ vertically opposite to $\angle 4$?

Ans: Yes,$\angle 1$ and$\angle 4$are formally by the intersection of two straight lines AB and CD.

vi) What is the vertically opposite angle of $\angle 5$ ?

Ans: $\angle COB$is the vertically opposite angle of $\angle 5$.Because these two angles are formed by the intersection of two straight lines AB and CD.

10. Indicate which pairs of angles are:

i) Vertically opposite angles.

Ans: After observing the figure we can say that,

$\angle 1$and $\angle 4$,$\angle 5$ and$\angle 2 + \angle 3$ are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.

ii) Linear pairs.

Ans: After observing the figure we can say that,

$\angle 1$and $\angle 5$,  $\angle 5$ and $\angle 4$as these are having a common vertex and also having the non common arms opposite to each other.

In the following figure, is $\angle 1$ adjacent to $\angle 2$? Give reasons.

Ans: Here, $\angle 1$and $\angle 2$are not adjacent angles. Because they do not lie on the same vertex.

11. Find the values of the angles x,y and z in each of the following :

i) 

Ans: Here, 

$\angle x = 55^\circ $  Because vertically opposite angles.

$\angle x + \angle y = 180^\circ$  ...[ linear pair]

$ = 55^\circ  + \angle y = 180^\circ $

$ = \angle y = 180^\circ  - 55^\circ $

$ = \angle y = 125^\circ $

Then, $\angle y = \angle z$ ….[ vertically opposite angles]

$\therefore \angle z = 125^\circ $

(ii)

Ans: Here,

$\angle z = 40^\circ $, Because vertically opposite angles.

$\angle y + \angle z = 180^\circ $   ….  ( linear pair)

$ = \angle y + 40^\circ  = 180^\circ $

$\begin{gathered}

   = \angle y = 180^\circ  - 40^\circ  \hfill \\

   \hfill \\ 

\end{gathered} $

$ = \angle y = 140^\circ $

Then, $40 + \angle x + 25 = 180^\circ $…( angles on straight line)

$\begin{gathered}

  65 + \angle x = 180^\circ  \hfill \\

   \hfill \\ 

\end{gathered} $

$\angle x = 180^\circ  - 65$

$\therefore \angle x = 115^\circ $

12. 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) Two angles forming a linear pair are __________ .

Ans: Supplementary

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

Ans: Linear pair

v) If two lines intersect at a point, then the vertically opposite angles are always _________.

Ans: Equal

vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.

Ans: Obtuse angles.

13. 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.

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

Opting for the NCERT solutions for Ex 5.1 Class 7 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.1 Class 7 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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