NCERT Solutions for Class 7 Maths 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

Other Study Material for CBSE Class 7 Maths Chapter 5

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.