NCERT Solutions for Class 7 Maths Chapter 5 - Lines And Angles

Exercise 5.1

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

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Ans: For finding complement angle we use = \[90{}^\circ -\] given angle

1. Complement of \[20{}^\circ  = 90{}^\circ -20{}^\circ =70{}^\circ \]

2. Complement of \[63{}^\circ =90{}^\circ -63{}^\circ =27{}^\circ \]

3. Complement of \[57{}^\circ =90{}^\circ -57{}^\circ =33{}^\circ \]

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

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Ans: For finding supplement angle we use = \[180{}^\circ -\] given angle

1. Supplement of \[105{}^\circ  = 180{}^\circ -105{}^\circ =75{}^\circ \]

2. Supplement of \[87{}^\circ =180{}^\circ -87{}^\circ =93{}^\circ \]

3. Supplement of \[154{}^\circ =180{}^\circ -154{}^\circ =26{}^\circ \]

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

Ans: If the sum of two angles is $180{}^\circ $, then they are called supplementary angles.

If the sum of two angles is $90{}^\circ ,$ then they are called complementary angles.

1. $65{}^\circ +115{}^\circ =180{}^\circ $

The sum of two angles is $180{}^\circ $. Thus, these are supplementary angles

2. $63{}^\circ +27{}^\circ =90{}^\circ $

The sum of two angles is $90{}^\circ $. Thus, these are complementary angles

(iii) $112{}^\circ +68{}^\circ =180{}^\circ $

The sum of two angles is $180{}^\circ $. Thus, these are supplementary angles

(iv) $130{}^\circ +50{}^\circ =180{}^\circ $

The sum of two angles is $180{}^\circ $. Thus, these are supplementary angles

(v) $45{}^\circ +45{}^\circ =90{}^\circ $

The sum of two angles is $90{}^\circ $. Thus, these are complementary angles

(vi) $80{}^\circ +10{}^\circ =90{}^\circ $

The sum of two angles is $90{}^\circ $. Thus, these are complementary angles

4. Find the angle which is equal to its complement:

Ans: Let one of the two complementary angles be $x$

 $ \therefore x+x=90{}^\circ  $ 

 $ 2x=90{}^\circ  $ 

 $ x=\frac{90}{2} $ 

 $ x=45{}^\circ  $ 

Thus, $45{}^\circ $is the angle equal to its complement.

5. Find the angle which is equal to its supplement:

Ans: Let one of the two supplementary angles be $x$

$ \therefore x+x=180{}^\circ  $

$ 2x=180{}^\circ  $ 

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

$ x=90{}^\circ  $

Thus, $90{}^\circ $is the angle equal to its complement.

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

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Ans: If $\angle 1$is decreased then, $\angle 2$will be increasing with the 

same measure in the way that both the angles still remain supplementary.

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

(i). acute

Ans: No, because sum of two acute angles is less than $180{}^\circ $

(ii). Obtuse

Ans: No, because sum of two obtuse angles is more than $180{}^\circ $

(iii). right?

Ans: Yes, because sum of two right angles is equal to $180{}^\circ $

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

Ans: Let the complementary angles be $x$and$y$, i.e., $x+y=90{}^\circ $

Given, $x>45{}^\circ $…………….$\left( i \right)$

Adding $y$to both sides in eq. $\left( i \right)$

 $ x+y>45{}^\circ +y $

 $ 90{}^\circ >45{}^\circ +y $ 

 $ 90{}^\circ -45>y $

 $ 45{}^\circ >y $

Thus, the complementary angle will be less than $45{}^\circ $

9. In the adjoining figure:

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

Ans: Yes, in $\angle AOE$, OC is common arm.

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

Ans: No, they have no non-common arms on opposite side of common arm.

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

Ans: Yes, they form linear pair.

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

Ans: Yes, they are supplementary.

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

Ans: Yes, they are vertically opposite angles.

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

Ans: Vertically Opposite Angle of $\angle 5$ is $\angle COB$

10. Indicate which pairs of angles are: 

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(i) Vertically opposite angles?

Ans: Vertically Opposite Angles are: 

$\angle 1,\angle 4$ and $\angle 5=\angle 2+\angle 3$

(ii) Linear pairs?

Ans: Linear Pairs are: 

$\angle 1+\angle 5$ and $\angle 5+\angle 4$

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

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Ans: $\angle 1$and $\angle 2$ are not adjacent angles because their vertex is not common.

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

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Ans: $\left( i \right)$$x=55{}^\circ $         (Vertically Opposite Angle)

Now, $55{}^\circ +y=180{}^\circ $ (Linear Pair)

 $ y=180{}^\circ -55{}^\circ  $

 $ y=125{}^\circ  $

 As, 

 $ y=z $ 

 $ y=z=125{}^\circ  $ 

Hence, $x=55{}^\circ ,y=125{}^\circ $and $z=125{}^\circ $

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Ans: $\left( ii \right)$$40{}^\circ +x+25{}^\circ =180{}^\circ $

$ \Rightarrow 65{}^\circ +x=180{}^\circ  $ 

$ \Rightarrow x=180{}^\circ -65{}^\circ $\ 

$ \Rightarrow x=115{}^\circ  $

Now, $40{}^\circ +y=180{}^\circ $       (Linear Pair)

 $ \Rightarrow y=180{}^\circ -40{}^\circ  $ 

 $ \Rightarrow y=140{}^\circ  $ 

Also, $y+z=180{}^\circ $         (Linear Pair)

$\Rightarrow 140{}^\circ +z=180{}^\circ $     ($y=140{}^\circ $, solved above)

 $ \Rightarrow z=180{}^\circ -140{}^\circ  $

 $ \Rightarrow z=40{}^\circ  $ 

Thus, $x=115{}^\circ ,y=140{}^\circ $and $z=40{}^\circ $

13. 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

(iv). If two adjacent angles are supplementary, they form a _______________.

Ans: Linear Pair

(v). If two lines intersect 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

14. In the adjoining figure, name the following pairs of angles:

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(i). Obtuse vertically opposite angles.

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

(ii). Adjacent complementary angles.

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

(iii). Equal supplementary angles.

Ans: In the given figure, $\angle EOB$ and $\angle EOD$ are equal supplementary angles

(iv). Unequal supplementary angles. 

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

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

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

Class –VII Mathematics (Ex. 5.2) 

Questions 

1. State the property that is used in each of the following statements:

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(i). If $a$$\parallel $$b$, then $\angle 1$ = $\angle 5$.

Ans: Given, $\angle 1$ 

than $\angle 1$ = $\angle 5$, (Corresponding Angle)

If the two parallel ($a$$\parallel $$b$) lines cut by a transversal ($b.$),

then each pair of corresponding angles will be equal in measure.

(ii). If ∠ 4 = ∠ 6, then $a$$\parallel $$b$.

Ans: Given, $\angle 4=\angle 6$ (Alternate Interior Angles)

than, $a$$\parallel $$b$

When a transversal ($b.$) cut two lines such that pairs of alternate interior angles are equal, then the lines will be parallel $a$$\parallel $$b$.

(iii). If $\angle 4+\angle 5=180{}^\circ $, then $a$$\parallel $$b$.

Ans: Given, $\angle 4+\angle 5=180{}^\circ $,

Then $a$$\parallel $$b$

When a transversal ($b.$) cut two lines such that pairs of interior angles on the same side of transversal are supplementary ($\angle 4+\angle 5=180{}^\circ $), the lines have to be parallel ($a$$\parallel $$b$).

2. In the adjoining figure, identify:

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(i). the pairs of corresponding angles.

Ans: The pair of corresponding angles are: 

($\angle 1,\angle 5$), ($\angle 2,\angle 6$), (\[\angle 4,\angle 8\]) & ($\angle 3,\angle 7$)

(ii). the pairs of alternate interior angles.

Ans: The pair of alternate interior angles are:

($\angle 3,\angle 5$) & ($\angle 2,\angle 8$)

(iii). the pairs of interior angles on the same side of the transversal.

Ans: The pair of interior angles on the same side of the transversal are: 

($\angle 3,\angle 8$) & ($\angle 2,\angle 5$)

(iv). the vertically opposite angles.

Ans: The vertically opposite angles are: 

($\angle 1,\angle 3$), ($\angle 2,\angle 4$), ($\angle 6,\angle 8$) & ($\angle 5,\angle 7$)

3. In the adjoining figure, \[p\]$\parallel $$q$. Find the unknown angles.

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Ans: Given, \[p\]$\parallel $$q$ and is cut by a transversal line

$\therefore $ $125{}^\circ +\angle e=180{}^\circ $ (Linear Pair)

$ \Rightarrow \angle e=180{}^\circ -125{}^\circ  $

$ \Rightarrow \angle e=55{}^\circ  $ 

Now, $\angle e=\angle f=55{}^\circ $ (Vertically Opposite Angles)

So, \[\angle f=\angle a=55{}^\circ \] (Alternate Interior Angles)

$\Rightarrow \angle a+\angle b=180{}^\circ $ (Linear Pair)

\[

 $ \Rightarrow 55{}^\circ +\angle b=180{}^\circ  $ 

 $ \Rightarrow \angle b=180{}^\circ -55{}^\circ  $

 $ \Rightarrow \angle b=125{}^\circ  $

\]

Now, \[

 $ \angle a=\angle c=55{}^\circ  $ 

$ \angle b=\angle d=125{}^\circ  $

\] (Vertically Opposite Angles)

Hence, \[\angle a=55{}^\circ ,\angle b=125{}^\circ ,\angle c=55{}^\circ ,\angle d=125{}^\circ ,\angle e=55{}^\circ \And \angle f=55{}^\circ \]

4. Find the values of x in each of the following figures if \[l\parallel m\].

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Ans: \[(i)\] Given, \[l\parallel m\]and t is transversal line. 

$\therefore $ Interior vertically opposite angle between lines \[l\]and\[t\]

$\therefore $ $110{}^\circ +x=180{}^\circ $ (Supplementary Angles)

$ x=180{}^\circ -110{}^\circ  $ 

$ x=70{}^\circ  $ 

\[(ii)\] Given, \[l\parallel m\]and t is transversal line.

$x+2x=180{}^\circ $ (Interior Opposite Angles)

$ 3x=180{}^\circ  $

$ x=\frac{180{}^\circ }{3} $

$x=60{}^\circ $

\[(iii)\] Given, \[l\parallel m\] and \[a\parallel b\]

\[x=100{}^\circ \] (Corresponding Angles)

5. In the given figure, the arms of two angles are parallel. If ∆ABC = \[70{}^\circ \], then find:

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(i). ∠ DGC (ii) ∠ DEF

Ans: 

\[(i)\] Given, \[AB\]\[\parallel \]\[DE\] and BC is a transversal line and \[\angle \]ABC\[=70{}^\circ \]

$\therefore $ \[\angle \]ABC\[=\]\[\angle \]DGC\[=70{}^\circ \] (Corresponding Angles)

\[\angle \]DGC\[=70{}^\circ \]

\[(ii)\] Given, \[BC\]\[\parallel \]\[DF\] and DE is a transversal line and \[\angle \]DGC\[=70{}^\circ \]

\[\angle \]DGC\[=\]\[\angle \]DEF\[=70{}^\circ \] (Corresponding Angles)

\[\angle \]DEF\[=70{}^\circ \]

6. In the given figures below, decide whether l is parallel to m.

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Ans: \[(i)\] \[126{}^\circ +44{}^\circ =170{}^\circ \]

l is not parallel to m because sum of interior opposite angles should 

be \[180{}^\circ \]

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\[(ii)\] \[75{}^\circ +75{}^\circ =150{}^\circ \]

l is not parallel to m because sum of angles is not obeying parallel

lines rules.

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\[(iii)\]\[57{}^\circ +123{}^\circ =180{}^\circ \]

l is parallel to m because sum of supplementary angles is \[180{}^\circ \]

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\[(iv)\]\[98{}^\circ +72{}^\circ =170{}^\circ \]

l is not parallel to m because sum of angles is not obeying parallel

lines rules.

NCERT Solutions for Class 7 Maths Chapter 5 PDF Download

NCERT solutions for class 7 Maths chapters are clearly explained with easy language and are available in PDF format on the official website of Vedantu. Also, students can avail these solutions with a basic internet connection and an electronic device, so that they can practice whenever they want at their own pace. NCERT solutions for the below topics of class 7 chapter 5 Maths covered in the PDF solved by the expert teachers.

Important Topics Under NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Chapter 5 of the Class 7 Maths syllabus is ‘Lines and Angles’. This chapter covered in the class 7 Maths syllabus has 4 major sections or topics. In order to learn from and relate to this crucial chapter in mathematics, we advise students to go through these individual subtopics that come under this chapter on Lines and Angles. 

We have provided the following list of important topics that are covered under this chapter so that students can get acquainted with the necessary concepts that have been used in the provided NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles.

• Introduction

• Related Angles

1. Complementary Angles

2. Supplementary Angles

3. Adjacent Angles

4. Linear Pairs

5. Vertically Opposite Angles

• Pairs of Lines

1. Intersecting Lines

2. Transversal

3. Angles Made by Transversal

4. Transversal of Parallel Lines

• Checking for Parallel Lines

We recommend that students read through each of these topics carefully and then get on to attempt and practise the NCERT solutions that we have provided for this chapter on Lines and Angles.

List of Exercises in Class 7 Maths Chapter 5:

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

5.1 Introduction

Students are introduced to this chapter by remembering the ray, line, line segment and angle. NCERT Solutions for Class 7 Maths PDF provides all the definitions. A ray has no endpoints in both directions. If there is an endpoint in one direction, we call it a line. Coming to the line segment, it has end-points on both sides. The current crucial topic is Angles. When two lines or line segments intersect each other, an angle is formed. With our well-designed solutions, students can attain a better understanding of the topic without referring to other books.

• Exercise 5.1 with 14 Problems (4 are Long Answers, and 10 are Short Answers).

5.2 Related Angles

Here, students can learn about various kinds of relative angles. Students can try to solve problems on each type of angle so that it gives them knowledge about their properties too.

• Exercise 5.2 with Six Sums  (2 are Short Answers, and 4 are Long Answers).

5.2.1 Complementary Angles

In this section, students can learn new topics like complementary angles and their properties and other kinds, etc. The law is that the sum of two supplementary angles is 90°. If an angle between two lines is 90°, we can say one angle is a complement to the other angle.

5.2.2 Supplementary Angles

The next relative angle available in the NCERT Solutions for Class 7 Maths Chapter 5 PDF book on the official website is the supplementary angles. Contrary to the complementary aspects, the sum of the two angles is 180°. Then they are called supplement angles.

5.2.3 Adjacent Angles

If any two angles have a common vertex and arm on any one side, they are called adjacent angles. The pages in a book, the car stereo are the best examples provided for students in the NCERT Solutions for Class 7 Maths Chapter 5 PDF books on the official website of Vedantu.

5.2.4 Linear Pairs

In this section, students can come across the concept of linear pairs. A pair of adjacent angles having rays in their non-common sides are nothing but linear pairs.

5.2.5 Vertically Opposite Angles

Students are asked to observe scissors, laundry stands, etc. to learn about these vertically opposite angles. An experiment with pencils is explained in NCERT Solutions for Class 7 Maths Chapter 5 PDF. When the two lines are intersecting each other, two equal and opposite angles are formed in a vertical direction.

5.3 Pairs of Lines

Now, students of Class 7 will learn about the remaining half of the chapter, which is about lines, its types and properties with examples and explanations.

5.3.1 Intersecting Lines

The first concept which students have to learn is Intersecting Lines. If two lines touch each other or meet at one point, those lines are called Intersecting lines and the touching point is called the point of intersection.

5.3.2 Transversal

It is an extension of Intersecting lines. If two or more lines intersect at more than one point, it is known as Transversal. Students can understand more clearly by reading the PDF available in NCERT Solutions for Class 7 Maths Chapter 5 with examples like railway lines and crossing multiple roads.

5.3.3 Angles made by Transversal

Here, students can understand the interrelation of lines and angles. When two lines act as Transversal, students can observe eight kinds of different angles formed with these lines. All the angles are different from each other. Some are interior, exterior, adjacent angles and even corresponding angles.

5.3.4 Transversal of Parallel Lines

In this topic, students will come to know the variations of parallel lines, if they are transversal. If Transversal cuts two parallel lines, each pair of corresponding angles and alternate interior angles are equal. Also, the pair of interior angles on the transversal side are supplementary to each other. So, a simple intersection can cause many angles and can change their properties.

5.4 Checking for Parallel Lines

So far, students learned to find angles based on the lines. And now, students can try to learn about the lines based on the angles formed, i.e. vice versa of the previous topic. If two lines are transversal and the corresponding angles are equal, the lines are parallel to each other.

Key Features of NCERT Solutions for Class 7 Maths Chapter 5

NCERT Solution for Class 7 Maths Chapter 5 PDF available on Vedantu is highly beneficial to students. In this electronic generation, students are more competitive and knowledgeable. To enhance your abilities, make good use of well-designed NCERT Solutions for Class 7 Maths Lines and Angles chapter on the official website of Vedantu. It is very beneficial to all students for further reference along with the class and to get more information.

• Our NCERT Solutions are well-explanatory and cover all the concepts.

• Our solutions are available in easy-to-understand and simple language prepared by the subject experts to reach all students.

• It enhances student’s knowledge which helps to attend competitive exams in maths and boost their self-confidence.

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