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

### NCERT Solutions for Class 7 Maths Chapter 5 – Exercise 5.1

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

Note: When the sum of the measures of two angles is 90°, then the angles are called complementary angles.

Complement = 90^{o} – 20^{o}= 70^{o}

Complement = 90^{ o} – 63^{ o}= 27^{ o}

Complement = 90^{ o} – 57^{ o}= 33^{ o}

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

** **Note: When the sum of the measures of two angles is 180°, the angles are called supplementary angles.

Supplement = 180^{ o} – 105^{ o}= 75^{ o}

Supplement = 180^{ o} – 87^{ o}= 93^{ o}

Supplement = 180^{ o} – 154^{ o}= 26^{ o}

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

Note: The sum of the measures of complementary angles is 90^{ o} and that of supplementary angles is 180^{ o}

i) 65^{ o}, 115^{ o}65^{ o} + 115^{ o} = 180^{ o}Supplementary Angles

ii) 63^{ o},27^{ o}63^{ o} + 27^{ o} = 90^{o}Complementary Angles

iii) 112^{ o}, 68^{ o}112^{ o} + 68^{ o} = 180^{ o}Supplementary Angles

iv) 130^{ o},50^{ o}130^{ o} + 50^{ o} = 180^{ o}Supplementary Angles

v) 45^{ o}, 45^{ o}45^{ o} +45^{ o} = 90^{ o}Complementary Angles

vi) 80^{ o},10^{ o}80^{ o} + 10^{ o} = 90^{ o}Complementary Angles

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

Let the angle be X

Given the complement of X is X

We know that the sum of the measures of complementary angles is 90^{ o}Therefore, X^{ o} + X^{ o} = 90^{ o}2X^{ o} = 90^{ o}X^{ o} =

X = 45^{ o}Thus, 45^{ o }is equal to its complement.

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

Let the angle be Y

Given the supplement of Y is Y

We know that the sum of the measures of supplementary angles is 180^{ o}Therefore, Y^{o} + Y^{ o} = 180^{o}2Y^{ o} = 180^{o}Y^{o} =

Y^{o} = 90^{o}Thus, 90^{ o }is equal to its supplement.

**6. In the given figure, ****∠****1 and ****∠****2 are supplementary angles. If ****∠****1 is decreased, what changes should take place in ****∠****2 so that both the angles still remain supplementary.**

Given : ∠1 and ∠2 are supplementary angles i.e ∠1 + ∠2 = 180^{o}If ∠1 is reduced by say x^{o} then ∠2 should be increased by x^{o} so that the angles still remain supplementary

i.e ∠1 – x^{o} + ∠2 + x^{o} = 180^{o }

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

**i) Acute?**

No.

Acute angles are angles that are less than 90^{o}Consider the sum of largest acute angle

89^{o} + 89^{o} = 178^{o} ≠ 180^{o}

**ii) Obtuse?**

No.

Obtuse angles are angles that are greater than 90^{o} and less than 180^{o}Consider the sum of the smallest obtuse angle

91^{o} + 91^{o} = 182^{o} > 180^{o}

**iii) Right?**

Yes.

90^{o} + 90^{o} = 180^{o}Therefore, two right angles are supplementary angles.

**8. An angle is greater than 45**^{o}**. Is its complementary angle greater than 45**^{o}** or equal to 45**^{o}** or less than 45**^{o}**? **

** **Given an angle X > 45^{o}And complement of X is 90^{o} – X

i.e X > 45^{o} implies -X < -45^{o}Add 90^{o }on both sides

90^{o} – X < 90 – 45^{o}90^{o} – X < 45^{o}Clearly, the complementary angle of X is less than 45^{o}

**9. In the adjoining figure:**

i) Is ∠1 adjacent to ∠2?

Yes, because:

Common vertex = O

Common arm = OC

AO and OE are on either side of OC

ii) Is ∠AOC adjacent to ∠AOE?

No,

∠AOC = ∠1 and ∠AOE = ∠1 + ∠2

Adjacent angles have no common interior points, here, both the angles have ∠1 as common interior point.

iii) Do ∠COE and ∠EOD form a linear pair?

Yes.

They form a liner pair because, the non-common arm arms OC and OD are opposite rays.

iv) Are ∠BOD and ∠DOA supplementary?

Yes.

∠BOD and ∠DOA are linear pairs and angles in linear pairs are supplementary.

v) Is ∠1 vertically opposite to ∠4?

Yes. AB and CD intersect at O, therefore ∠1 are ∠4 are vertically opposite angles.

vi) What is the vertically opposite angle of ∠5?

AB and CD intersect at O.

∠AOD is vertically opposite to ∠COB

i.e ∠5 is vertically opposite to ∠COB = ∠2 + ∠3

**10. Indicate which pairs of angles are:**

i) Vertically opposite angles.

∠1 and ∠4

∠5 and ∠2 + ∠3

ii) Linear pairs

∠5 and ∠1

∠4 and ∠5

**11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.**

∠1 and ∠2 do not have a common vertex, hence they are not adjacent to each other.

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

**i)**

∠x = 55^{o} (Vertically opposite angles are equal)

∠x and ∠y are supplementary since they are linear pairs, therefore, ∠x + ∠y = 180^{o}∠y = 180^{o} – 55^{o}∠y = 125^{o}

∠z = 125^{o} (Vertically opposite angles are equal. Here ∠z and ∠y are vertically opposite to each other)

∠y + 40^{o} = 180^{o} [Linear pair of Angles]

y = 180^{o} – 40^{o}y = 140^{o}y and z form linear pair, implying that they are supplementary.

i.e y + z = 180^{o}z = 180^{o} – y

= 180^{o} – 140^{o}z = 40^{o}

Alternative Method: z = 40^{o} (Vertically opposite angles)

40^{o} + x + 25^{o} = 180^{o} [Angles on Straight line]

x + 65^{o} = 180^{o}x = 180^{o} – 65^{o}x = 115^{o}

**13. Fill in the blanks:**

i) If two angles are complementary, then the sum of their measures is __________.

Ans: 90^{o}

ii) If two angles are supplementary, then the sum of their measures is __________.

Ans: 180^{o}

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 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

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

i) Obtuse vertically opposite angles

Ans: ∠AOD and ∠BOC

ii) Adjacent complementary angles

Ans: ∠EOA and ∠AOB

iii) Equal supplementary angles

Ans: ∠EOD and ∠EOB

iv) Unequal supplementary angles

Ans: ∠EOA and ∠EOC, ∠DOC and ∠COB

v) Adjacent angles that do not form a linear pair

Ans: ∠EOD and ∠DOC, ∠AOE and ∠EOD, ∠AOB and ∠EOA

### NCERT Solutions for Class 7 Maths Chapter 5 – Exercise 5.2

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

i) If a || b, then ∠1 = ∠5.

Corresponding Angles Property

ii) If ∠4 = ∠6, then a || b.

Alternate Interior Angles Property

iii) If ∠4 + ∠5 = 180°, then a || b.

When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary.

**2. In the adjoining figure, identify **

i) the pairs of corresponding angles.

∠4 and ∠8

∠1 and ∠5

∠3 and ∠7

∠2 and ∠6

ii) the pairs of alternate interior angles.

∠3 and ∠5

∠2 and ∠8

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

∠3 and ∠8

∠2 and ∠5

iv) the vertically opposite angles

∠4 and ∠2

∠1 and ∠3

∠8 and ∠6

∠5 and ∠7

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

∠d = 125^{o} (125^{o }and ∠d are corresponding angles)

∠b = 125^{o} (∠d and ∠b are vertically opposite angles)

∠f = 180^{o} – 125^{o} [Linear Pair of Angles]

∠f = 55^{o}∠e = 55^{o} (∠f and ∠e are vertically opposite angles)

∠a = 55^{o} (∠f and ∠a are alternate angles)

∠c = 55^{o} (∠a and ∠c are vertically opposite angles)

**Note: You could cite various other appropriate reasons too.**

**4. Find the value of x in each of the following figures if l || m.**

Given l||m

∠QOL = 180^{o} – 110^{o} [Linear pair of angles]

∠QOL = 70^{o}x = 70^{o} [∠QOL and ∠OPM are Corresponding Angles]

Given l || m

x = 100^{o} (Corresponding angles)

**5. In the given figure, the arms of two angles are parallel. If ∠ABC = 70**^{o}**, then find**

i) ∠DGC

Given l || m

∠DGC = ∠ABC = 70^{o} (Corresponding angles)

ii) ∠DEF

Given p || q

∠DEF = ∠DGC = 70^{o} (Corresponding angles)

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

When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.

126^{o }+ 44^{o} = 170^{o} ≠180^{o}

Therefore, l is not parallel to m.

∠BOP = 75^{o}When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.

Here, ∠BOP + ∠CPO = 75^{o} + 75^{o}= 150^{o} ≠ 180^{o}Therefore, l is not parallel to m.

∠FOA = 180^{o} – 57^{o} = 123^{o}∠FOA = ∠OPB = 123^{o}When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.

Therefore, l is parallel to m

∠BPC = ∠OPD = 72^{o} [Vertically Opposite Angles]

When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.

∠OPD + ∠POE = 72^{o} + 98^{o}= 170^{o} ≠ 180^{o}Therefore, l is not parallel to m

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