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# NCERT Solutions for Class 7 Maths Chapter 5 - Lines and Angles Exercise 5.2

Last updated date: 17th Sep 2024
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## NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2 - FREE PDF Download

Ex 5.2 Class 7 of Chapter 5 in Class 7 Maths, dive deeper into the fascinating world of lines and angles. This exercise focuses on the fundamental properties and relationships between angles formed by intersecting lines. Let us explore concepts such as complementary and supplementary angles, vertically opposite angles, and the properties of parallel lines cut by a transversal in Class 7 Maths Ch 5 Ex 5.2. The NCERT class 7 Maths chapter 5 exercise 5.2 solutions, provided by Vedantu, offer detailed explanations and step-by-step solutions to the problems in Exercise 5.2. These solutions are designed to help students grasp the concepts thoroughly, making it easier to tackle similar problems independently.

Table of Content
1. NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2 - FREE PDF Download
2. Glance on NCERT Solutions Class 7 Maths Chapter 5 Exercise 5.2 | Vedantu
3. Access NCERT Solutions for Maths Class 7 Chapter 5 Lines and Angles Exercise 5.2
4. Class 7 Maths Chapter 5: Exercises Breakdown
5. Other Study Material for CBSE Class 7 Maths Chapter 5
6. Chapter-Specific NCERT Solutions for Class 7 Maths
FAQs

## Glance on NCERT Solutions Class 7 Maths Chapter 5 Exercise 5.2 | Vedantu

• Parallel Lines: Two lines that never meet, no matter how far they are extended in either direction.

• Transversal: A line that intersects two or more other lines at distinct points.

• Corresponding Angles: Angles that lie on the same side of the transversal and outside the parallel lines. (Marked as ∠1 and ∠5, ∠2 and ∠6, and so on in a diagram)

• Alternate Interior Angles: Angles that lie inside the parallel lines but on alternate sides of the transversal. (Marked as ∠2 and ∠8, ∠3 and ∠5 in a diagram)

• Interior Angles on the Same Side: Angles that lie inside the parallel lines on the same side of the transversal. (Marked as ∠2 and ∠5, ∠3 and ∠8 in a diagram.

• There are 6 questions in class 7 maths ex 5.2 which are fully solved by experts at Vedantu.

## Access NCERT Solutions for Maths Class 7 Chapter 5 Lines and Angles Exercise 5.2

Exercise 5.2

Refer to pages 7-13 for Exercise 5.2 in the PDF.

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

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

Ans: Corresponding angles property is used in the above statement.

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

Ans : Alternate interior angles property is used in the above statement.

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

Ans : Interior angles on the same side of transversal are supplementary.

2. In the adjoining figure, identify

i) The pairs of corresponding angles.

Ans : After observing the figure, the pairs of corresponding angles are,

\$\angle 1\$ and \$\angle 5\$, \$\angle 4\$ and \$\angle 8\$, \$\angle 2\$ and \$\angle 6\$, \$\angle 3\$ and \$\angle 7\$.

ii) The pairs of alternate interior angles.

Ans: After observing the figure, the pairs of alternate interior angles are,

\$\angle 2\$ and \$\angle 8\$, \$\angle 3\$ and \$\angle 5\$

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

Ans : After observing the figure, the pairs of interior angles on same side of transversal are,

\$\angle 2\$ and \$\angle 5\$, \$\angle 3\$ and \$\angle 8\$.

iv) The vertically opposite angles.

Ans : After observing the figure, the pairs of vertically opposite angles are,

\$\angle 1\$ and \$\angle 3\$, \$\angle 5\$ and \$\angle 7\$,\$\angle 2\$ and \$\angle 4\$,\$\angle 6\$ and \$\angle 8\$

3. In the adjoining figure, p||q. Find the unknown angle.

Ans: Here,

By observing the figure,

\$\angle d = 125^\circ \$            (corresponding angles)
Also, we know that linear pair is the sum of adjacent angles is 1800

Then,

\$ = \angle e +  + 125^\circ  = 180^\circ \$   (linear pair)

\$ = \angle e = 180^\circ  - 125^\circ \$

\$ = \angle e = 55^\circ \$

From the rule of vertically opposite angles,

\$\angle f = \angle e = 55^\circ \$

\$\angle b = \angle d = 125^\circ \$

By the property of corresponding angles,

\$\angle c = \angle f = 55^\circ \$

\$\angle a = \angle e = 55^\circ \$

4. Find the value of \$x\$in each of the following figures if \$l\parallel m\$.

(I)

Ans : Here, let us assume another angle on the line m be \$\angle y\$.

Then,

By the property of corresponding angles

\$\angle y = 110^\circ \$

As we know that linear pair is the sum of adjacent angles is \$180^\circ \$

Then,

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

\$ = \angle x + 110^\circ  = 180^\circ \$

\$ = \angle x = 180^\circ  - 110^\circ \$

\$ = \angle x = 70^\circ \$

(ii)

Ans: Here,

Given, \$l\parallel m\$ and t is the transversal line.

\$x + 2x = 180^\circ \$                  (Interior opposite angles)

\$ = 3x = 180^\circ \$

\$x = \dfrac{{180^\circ }}{3} = 60^\circ \$

(iii)

Ans : Here,

\$l\parallel m\$ , and \$a\parallel b\$

Therefore,

\$x = 100^\circ \$          (corresponding angles)

5. In the figure, the arms of two angles are parallel.

If \$\angle ABC = 70^\circ \$, then find

i) \$\angle DGC\$

Ans : Here, let us consider that \$AB\parallel DG\$

By the property of corresponding angles,

\$\angle DGC = \angle ABC\$

Then,

\$\angle DGC = 70^\circ \$

ii) \$\angle DEF\$

Ans: Here, let us consider that \$BC\parallel EF\$

DE is the transversal line intersecting BC and EF

By the property of corresponding angles,

\$\angle DEF = \angle DGC\$

Then,

\$\angle DEF = 70^\circ \$

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

(I)

Ans: Here, let us consider the two lines \$l\$ and \$m\$.

And n is the transversal line intersecting \$l\$ and \$m\$.

We know that the sum of interior angles on the same side of transversal is \$180^\circ \$

Then,

\$ = 126^\circ  + 44^\circ \$

\$ = 170^\circ \$

But, the sum of interior angles on the same side of transversal is not equal to

\$180^\circ \$.

So, line \$l\$ is not parallel to line \$m\$.

(ii)

Ans: Here, let us assume \$\angle x\$  be the vertically opposite angle formed due to the intersection of the straight line \$l\$ and transversal n,

Then,

\$\angle x = 75^\circ \$

Now, let us consider the two lines \$l\$ and \$m\$,

N is the transversal line intersecting \$l\$ and \$m\$.

As we know that the sum of interior angles on the same side of transversal is \$180^\circ \$.

Then,

\$ = 75^\circ  + 75^\circ \$

\$ = 150^\circ \$

But the sum of interior angles on the same side of transversal is not equal to \$180^\circ \$.

So, line \$l\$ is not parallel to line m.

(iii)

Ans: Here, let us assume \$\angle x\$ be the vertically opposite angle formed due to the intersection of the Straight line l and transversal line n,

Now, let us consider the two lines \$l\$ and m,

N is the transversal line \$l\$ and m.

As we know that the sum of interior angles on the same side of transversal is \$180^\circ \$.

Then,

\$ = 123^\circ  + \angle x\$

\$ = 123^\circ  + 57^\circ \$

\$ = 180^\circ \$

Therefore,  the sum of interior angles on the same side of transversal is equal to \$180^\circ \$

So, line \$l\$ is parallel to line \$m\$.

(iv)

Ans: Here, let us assume \$\angle x\$ be the angle formed due to the intersection of the Straight line \$l\$ and transversal line n,

As we know that linear pair is the sum of adjacent angles is equal to \$180^\circ \$.

\$ = \angle x + 98^\circ  = 180^\circ \$

\$ = \angle x = 180^\circ  - 98^\circ \$

\$ = \angle x = 82^\circ \$

Now, as we consider \$\angle x\$ and \$72^\circ \$ are the corresponding angles.

For l and m to be parallel to each other, corresponding angles should be equal.

But, in the given figure corresponding angles measure \$82^\circ \$ and \$72^\circ \$ respectively.

\$\therefore \$ Line \$l\$ is not parallel to line \$m\$.

## Conclusion

Class 7 Maths Chapter 5.2 focuses on the fundamental concepts of lines and angles, including the identification and measurement of angles, the properties of intersecting lines, and the relationships between various angles. This exercise is essential for building a solid foundation in geometry, which is critical for understanding more complex geometric principles in higher classes.

In previous years' exams, typically 2 to 3 questions have been asked from this class 7 maths ex 5.2, indicating its moderate importance in the overall curriculum.

## Class 7 Maths Chapter 5: Exercises Breakdown

 Exercise Number of Questions Exercise 5.1 10 Questions & Solutions

## Chapter-Specific NCERT Solutions for Class 7 Maths

Given below are the chapter-wise NCERT Solutions for Class 7 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

## FAQs on NCERT Solutions for Class 7 Maths Chapter 5 - Lines and Angles Exercise 5.2

1. What are complementary and supplementary angles in class 7 exercise 5.2?

Complementary angles are two angles whose sum is 90 degrees. For example, if one angle is 30 degrees, the other must be 60 degrees to be complementary. Supplementary angles are two angles whose sum is 180 degrees. For example, if one angle is 110 degrees, the other must be 70 degrees to be supplementary.

2. What are vertically opposite angles?

Vertically opposite angles are the angles opposite each other when two lines intersect. These angles are always equal. For example, if two lines intersect and form angles of 70 degrees and 110 degrees, the vertically opposite angles will also be 70 degrees and 110 degrees respectively.

3. How can we identify alternate interior angles?

Alternate interior angles are the pairs of angles formed on opposite sides of a transversal, but inside the two lines it intersects. These angles are equal when the lines are parallel. For instance, if two parallel lines are cut by a transversal, the angles on the inside, but on opposite sides of the transversal, are alternate interior angles.

4. What are corresponding angles?

Corresponding angles are the angles that occupy the same relative position at each intersection where a transversal crosses two lines. If the two lines are parallel, corresponding angles are equal. For example, if a transversal cuts across two parallel lines, each angle in one line corresponds to an angle in the same position in the other line.

5. What do you mean by the Corresponding angle in class 7 maths?

The angles created when a transversal intersects two parallel lines are known as corresponding angles. According to the corresponding angle postulate, if a transversal intersects two parallel lines, the corresponding angles must be congruent. In other words, the corresponding angles will always be equal if a transversal intersects two parallel lines. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and creating endless parallel railroad tracks.