**NCERT Solutions for Class 7 Maths**

Chapter 5 Lines and Angles

Exercise 5.1

Chapter 5 Lines and Angles

Exercise 5.1

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

**Answer **

(i) Complement angle of 20°=90° – 20°= 70°

(ii) Complement angle of 63°=90 – 63°= 27°

(iii) Complement angle of 57°= 90°- 57°= 33

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

**Answer**

(i) Supplement angle of 105° = 180° – 105°= 75°

(ii) Supplement angle of 87 = 180° – 87° = 93°

(iii) Supplement angle of 154° = 180° – 154°= 26°

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

**(i) 65º, 115º
(ii) 63º, 27º
(iii) 112º, 68º**

**(iv) 130º, 50º**

(v) 45º, 45º

(vi) 80º, 10º

(v) 45º, 45º

(vi) 80º, 10º

**Answer**

Firstly, find the sum of the given angles. If the sum of the angles is 90° then they are complementary and if the sum of the angles is 180° then they are supplementary.

∴ ∠x+ ∠y=65°+ 115°=180°

Hence, ∠x and ∠y are supplementary angles. (ii) Let ∠x=63° and ∠y= 27°

∴ ∠x+ ∠y= 63° + 27°= 90°

Hence, ∠x and ∠y are complementary angles. (iii) Let ∠x = 112° and y=68°

∴ ∠x+ ∠y=112° + 68° = 180°

Hence, ∠x and ∠y are supplementary angles. (iv) Let ∠x= 130° and ∠y = 50

∴ ∠x+∠y = 130°+50° = 180°

Hence, ∠x and ∠y are supplementary angles.

(v) Let ∠x=45° and ∠y=45°

∴ ∠x+ ∠y = 45°+45° = 90

Hence, ∠x and ∠y are complementary angles.

(vi) Let ∠x=80° and ∠y= 10°

∴ ∠x+ ∠y = 80°+10° = 90°

Hence, ∠x and ∠y are complementary angles.

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

**Answer**

Let the measure of the required angle be x^{o}.

We know that, sum of measures of complementary angle pair is 90^{o}.

Then,

= x + x = 90^{o
}= 2x = 90^{o
}= x = 90/2

= x = 45^{o
}Hence, the required angle measures is 45^{o}.

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

**Answer**

Let the measure of the required angle be x^{o}.

We know that, sum of measures of supplementary angle pair is 180^{o}.

Then,

= x + x = 180^{o
}= 2x = 180^{o
}= x = 180/2

= x = 90^{o
}Hence, the required angle measures is 90^{o}.

**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.**

**Answer**

From the question, it is given that,

∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 must be increased by the same value.

Hence, this angle pair remains supplementary.

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

**(i) acute? (ii) obtuse? (iii) right?**

**Answer**

(i) No. If two angles are acute, means less than 90^{o}, the two angles cannot be supplementary.

Because, their sum will be always less than 90^{o}.

(ii) No. If two angles are obtuse, means more than 90^{o}, the two angles cannot be supplementary.

Because, their sum will be always more than 180^{o}.

(iii) Yes. If two angles are right, means both measures 90^{o}, then two angles can form a supplementary pair.

∴ 90^{o }+ 90^{o} = 180

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

**Answer**

Let us assume the complementary angles be p and q,

We know that, sum of measures of complementary angle pair is 90^{o}.

Then,

= p + q = 90^{o
}It is given in the question that p > 45^{o
}Adding q on both the sides,

= p + q > 45^{o }+ q

= 90^{o} > 45^{o }+ q

= 90^{o} – 45^{o} > q

= q < 45^{o
}Hence, its complementary angle is less than 45^{o}.

**9. In the adjoining figure:**

**(i) Is ∠1 adjacent to ∠2?**

**(ii) Is ∠AOC adjacent to ∠AOE?**

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

**(iv) Are ∠BOD and ∠DOA supplementary?**

**(v) Is ∠1 vertically opposite to ∠4?**

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

**Answer**

(i) By observing the figure we came to conclude that,

Yes, as ∠1 and ∠2 having a common vertex i.e. O and a common arm OC.

Their non-common arms OA and OE are on both the side of common arm.

(ii) By observing the figure, we came to conclude that,

No, since they are having a common vertex O and common arm OA.

But, they have no non-common arms on both the side of the common arm.

(iii) By observing the figure, we came to conclude that,

Yes, as ∠COE and ∠EOD having a common vertex i.e. O and a common arm OE.

Their non-common arms OC and OD are on both the side of common arm.

(iv) By observing the figure, we came to conclude that,

Yes, as ∠BOD and ∠DOA having a common vertex i.e. O and a common arm OE.

Their non-common arms OA and OB are opposite to each other.

(v) Yes, ∠1 and ∠2 are formed by the intersection of two straight lines AB and CD.

(vi) ∠COB is the vertically opposite angle of ∠5. Because these two angles are formed by the intersection of two straight lines AB and CD.

**10. Indicate which pairs of angles are:
(i) Vertically opposite angles. (ii) Linear pairs.**

**Answer**

∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines. (ii) By observing the figure we can say that,

∠1 and ∠5, ∠5 and ∠4 as these are having a common vertex and also having non common arms opposite to each other.

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

**Answer**

∠1 and ∠2 are not adjacent angles. Because, they are not lie on the same vertex.

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

**Answer**

(i) ∠x = 55^{o}, because vertically opposite angles.

∠x + ∠y = 180^{o} … [∵ linear pair]

= 55^{o} + ∠y = 180^{o
}= ∠y = 180^{o} – 55^{o
}= ∠y = 125^{o
}Then, ∠y = ∠z … [∵ vertically opposite angles]

∴ ∠z = 125^{o}

(ii) ∠z = 40^{o}, because vertically opposite angles.

∠y + ∠z = 180^{o} … [∵ linear pair]

= ∠y + 40^{o} = 180^{o
}= ∠y = 180^{o} – 40^{o
}= ∠y = 140^{o
}Then, 40 + ∠x + 25 = 180^{o} … [∵angles on straight line]

65 + ∠x = 180^{o
}∠x = 180^{o} – 65

∴ ∠x = 115^{o}

**13. Fill in the blanks:**

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

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

**(iii) Two angles forming a linear pair are _______________.**

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

**(v) If two lines intersect at a point, then the vertically opposite angles are always _____________.**

**(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 __________.**

**Answer**

(i) If two angles. are complementary, then the sum of their measures is **90°**

(ii) If two angles are supplementary, then the sum of their measures is **180°**

(iii) Two angles forming a linear pair are **adjacent angles or supplementary**.

(iv) If two adjacent angles are supplementary, then they form a **linear pair**.

(v) If two lines intersect at a point, then the vertically opposite angles are always **equal**.

(vi) If two lines intersect at a point and one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are **obtuse angles**.

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

**(i) Obtuse vertically opposite angles**

**(ii) Adjacent complementary angles**

**(iii) Equal supplementary angles**

**(iv) Unequal supplementary angles**

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

**Answer**

(i) A pair of obtuse vertically opposite angles are ∠AOD and ∠BOC.

(ii) Adjacent complementary angles are ∠AOB and ∠AOE.

(iii) Equal supplementary angles are ∠BOE and ∠EOD.

(iv) Unequal supplementary angles are ∠E0A and ∠E0C.

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

∠AOB, ∠AOE, ∠AOE, ∠EOD, ∠EOD, ∠COD

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