NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

Exercise 5.1: Pairs of Angles

• Complementary and Supplementary Angles: Problems where students determine if angles are complementary or supplementary and calculate the unknown angles.

• Adjacent and Vertically Opposite Angles: Exercises focusing on identifying and calculating adjacent and vertically opposite angles in given diagrams.

Exercise 5.2: Transversal and Angles Formed

• Angles Formed by a Transversal: Questions about identifying corresponding, alternate interior, and alternate exterior angles when a transversal cuts through parallel lines.

• Calculations and Proofs: Problems involving calculating unknown angles and proving certain angle properties using theorems.

Access NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles

Exercise 5.1

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

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:

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, $\mathrm{\angle }1$ and $\mathrm{\angle }2$ are supplementary angles $\mathrm{\angle }1$ is decreased, what changes should take place in $\mathrm{\angle }2$ so that both the angles still remain supplementary?

Ans: If $\mathrm{\angle }1$is decreased then, $\mathrm{\angle }2$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. 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

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

(i). Obtuse vertically opposite angles.

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

(ii). Adjacent complementary angles.

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

(iii). Equal supplementary angles.

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

(iv). Unequal supplementary angles. 

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

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

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

Exercise  5.2 

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

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

Ans: Given, $\mathrm{\angle }1$ 

than $\mathrm{\angle }1$ = $\mathrm{\angle }5$, (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, $\mathrm{\angle }4=\mathrm{\angle }6$ (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 $\mathrm{\angle }4+\mathrm{\angle }5=180{}^{\circ }$, then $a$$\parallel$$b$.

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

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 ($\mathrm{\angle }4+\mathrm{\angle }5=180{}^{\circ }$), the lines have to be parallel ($a$$\parallel$$b$).

2. In the adjoining figure, identify:

(i). the pairs of corresponding angles.

Ans: The pair of corresponding angles are: 

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

(ii). the pairs of alternate interior angles.

Ans: The pair of alternate interior angles are:

($\mathrm{\angle }3,\mathrm{\angle }5$) & ($\mathrm{\angle }2,\mathrm{\angle }8$)

(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: 

($\mathrm{\angle }3,\mathrm{\angle }8$) & ($\mathrm{\angle }2,\mathrm{\angle }5$)

(iv). the vertically opposite angles.

Ans: The vertically opposite angles are: 

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

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

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

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

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

$\Rightarrow \mathrm{\angle }e=55{}^{\circ }$ 

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

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

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

\[

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

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

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

\]

Now, \[

 $\mathrm{\angle }a=\mathrm{\angle }c=55{}^{\circ }$ 

$\mathrm{\angle }b=\mathrm{\angle }d=125{}^{\circ }$

\] (Vertically Opposite Angles)

Hence, $$\mathrm{\angle }a=55{}^{\circ },\mathrm{\angle }b=125{}^{\circ },\mathrm{\angle }c=55{}^{\circ },\mathrm{\angle }d=125{}^{\circ },\mathrm{\angle }e=55{}^{\circ }\mathrm{\&}\mathrm{\angle }f=55{}^{\circ }$$

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

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:

(i). ∠ DGC (ii) ∠ DEF

Ans: 

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

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

$$\mathrm{\angle }$$DGC$$=70{}^{\circ }$$

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

$$\mathrm{\angle }$$DGC$$=$$$$\mathrm{\angle }$$DEF$$=70{}^{\circ }$$ (Corresponding Angles)

$$\mathrm{\angle }$$DEF$$=70{}^{\circ }$$

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

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

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

be $$180{}^{\circ }$$

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

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

lines rules.

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

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

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

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

lines rules.

Overview of Deleted Syllabus for CBSE Class 7 Maths Lines and Angles

Class 7 Maths Chapter 5: Exercises Breakdown

Conclusion

NCERT Maths class 7 chapter 5 - Lines and Angles is crucial for building a solid understanding of geometry. Focus on learning the different types of angles and pairs of angles, along with the properties of parallel lines. Key concepts include acute, obtuse, and right angles, as well as complementary and supplementary angles. Last year's exam featured around 3–4 questions from this chapter, highlighting both theory and practical problems. Regular practice with NCERT Solutions will ensure you grasp these concepts well. Keep studying and clarifying your doubts to excel in geometry!

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