NCERT Solutions for Class 7 Maths Exercise 5.1 Chapter 5 Lines and Angles in simple PDF are given here. This exercise of NCERT Solutions for Class 7 Maths Chapter 5 has topics related to complementary angles, supplementary angles, adjacent angles, linear pair and vertically opposite angles. When the sum of two angles is 90 degrees, such angles are complementary angles. When the sum of two angles is 180 degrees, such angles are supplementary angles. When the angles have a common vertex and a common arm but no common interior points, such angles are adjacent angles. Learn more about these topics by solving the questions of NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles with the help of solutions provided here.

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### Access Answers to NCERT Solutions Class 7 Maths Chapter 5 â€“ Lines and Angles Exercise 5.1

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

**(i)**

** **

**Solution:-**

Two angles are said to be complementary if the sum of their measures is 90^{o}.

The given angle is 20^{o}

Let the measure of its complement be x^{o}.

Then,

= x + 20^{o} = 90^{o}

= x = 90^{o} â€“ 20^{o}

= x = 70^{o}

Hence, the complement of the given angle measures 70^{o}.

**(ii)**

**Solution:-**

Two angles are said to be complementary if the sum of their measures is 90^{o}.

The given angle is 63^{o}

Let the measure of its complement be x^{o}.

Then,

= x + 63^{o} = 90^{o}

= x = 90^{o} â€“ 63^{o}

= x = 27^{o}

Hence, the complement of the given angle measures 27^{o}.

**(iii)**

**Solution:-**

Two angles are said to be complementary if the sum of their measures is 90^{o}.

The given angle is 57^{o}

Let the measure of its complement be x^{o}.

Then,

= x + 57^{o} = 90^{o}

= x = 90^{o} â€“ 57^{o}

= x = 33^{o}

Hence, the complement of the given angle measures 33^{o}.

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

**(i)**

**Solution:-**

Two angles are said to be supplementary if the sum of their measures is 180^{o}.

The given angle is 105^{o}

Let the measure of its supplement be x^{o}.

Then,

= x + 105^{o} = 180^{o}

= x = 180^{o} â€“ 105^{o}

= x = 75^{o}

Hence, the supplement of the given angle measures 75^{o}.

**(ii)**

**Solution:-**

Two angles are said to be supplementary if the sum of their measures is 180^{o}.

The given angle is 87^{o}

Let the measure of its supplement be x^{o}.

Then,

= x + 87^{o} = 180^{o}

= x = 180^{o} â€“ 87^{o}

= x = 93^{o}

Hence, the supplement of the given angle measures 93^{o}.

**(iii)**

**Solution:-**

Two angles are said to be supplementary if the sum of their measures is 180^{o}.

The given angle is 154^{o}

Let the measure of its supplement be x^{o}.

Then,

= x + 154^{o} = 180^{o}

= x = 180^{o} â€“ 154^{o}

= x = 26^{o}

Hence, the supplement of the given angle measures 93^{o}.

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

**(i) 65 ^{o}, 115^{o}**

**Solution:-**

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 65^{o} + 115^{o}

= 180^{o}

If the sum of two angle measures is 180^{o}, then the two angles are said to be supplementary.

âˆ´These angles are supplementary angles.

**(ii) 63 ^{o}, 27^{o}**

**Solution:-**

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 63^{o} + 27^{o}

= 90^{o}

If the sum of two angle measures is 90^{o}, then the two angles are said to be complementary.

âˆ´These angles are complementary angles.

**(iii) 112 ^{o}, 68^{o}**

**Solution:-**

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 112^{o} + 68^{o}

= 180^{o}

If the sum of two angle measures is 180^{o}, then the two angles are said to be supplementary.

âˆ´These angles are supplementary angles.

**(iv) 130 ^{o}, 50^{o}**

**Solution:-**

Then,

= 130^{o} + 50^{o}

= 180^{o}

If the sum of two angle measures is 180^{o}, then the two angles are said to be supplementary.

âˆ´These angles are supplementary angles.

**(v) 45 ^{o}, 45^{o}**

**Solution:-**

Then,

= 45^{o} + 45^{o}

= 90^{o}

If the sum of two angle measures is 90^{o}, then the two angles are said to be complementary.

âˆ´These angles are complementary angles.

**(vi) 80 ^{o}, 10^{o}**

**Solution:-**

Then,

= 80^{o} + 10^{o}

= 90^{o}

If the sum of two angle measures is 90^{o}, then the two angles are said to be complementary.

âˆ´These angles are complementary angles.

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

**Solution:-**

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 angles which is equal to its supplement.**

**Solution:-**

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, âˆ 1 and âˆ 2 are supplementary angles. If âˆ 1 is decreased, what changes should take place in âˆ 2 so that both angles still remain supplementary.**

**Solution:-**

From the question, it is given that,

âˆ 1 and âˆ 2 are supplementary angles.

If âˆ 1 is decreased, then âˆ 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?**

**Solution:-**

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). Obtuse?**

**Solution:-**

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). Right?**

**Solution:-**

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

âˆ´90^{o }+ 90^{o} = 180

**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}?**

**Solution:-**

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} â€“ 45^{o} > q

= q < 45^{o}

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

**9. In the adjoining figure:**

**(i) Is âˆ 1 adjacent to âˆ 2?**

**Solution:-**

By observing the figure we came to conclude that,

Yes, as âˆ 1 and âˆ 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) Is âˆ AOC adjacent to âˆ AOE?**

**Solution:-**

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) Do âˆ COE and âˆ EOD form a linear pair?**

**Solution:-**

By observing the figure, we came to conclude that,

Yes, as âˆ COE and âˆ 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) Are âˆ BOD and âˆ DOA supplementary?**

**Solution:-**

By observing the figure, we came to conclude that,

Yes, as âˆ BOD and âˆ 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) Is âˆ 1 vertically opposite to âˆ 4?**

**Solution:-**

Yes, âˆ 1 and âˆ 2 are formed by the intersection of two straight lines AB and CD.

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

**Solution:-**

âˆ COB is the vertically opposite angle of âˆ 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.**

**Solution:-**

By observing the figure we can say that,

âˆ 1 and âˆ 4, âˆ 5 and âˆ 2 + âˆ 3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.

**(ii) Linear pairs.**

**Solution:-**

By observing the figure we can say that,

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

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

**Solution:-**

âˆ 1 and âˆ 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:**

**(i)**

**Solution:-**

âˆ x = 55^{o}, because vertically opposite angles.

âˆ x + âˆ y = 180^{o} â€¦ [âˆµ linear pair]

= 55^{o} + âˆ y = 180^{o}

= âˆ y = 180^{o} â€“ 55^{o}

= âˆ y = 125^{o }

Then, âˆ y = âˆ z â€¦ [âˆµ vertically opposite angles]

âˆ´ âˆ z = 125^{o}

**(ii)**

**Solution:-**

âˆ z = 40^{o}, because vertically opposite angles.

âˆ y + âˆ z = 180^{o} â€¦ [âˆµ linear pair]

= âˆ y + 40^{o} = 180^{o}

= âˆ y = 180^{o} â€“ 40^{o}

= âˆ y = 140^{o }

Then, 40 + âˆ x + 25 = 180^{o} â€¦ [âˆµangles on straight line]

65 + âˆ x = 180^{o }

âˆ x = 180^{o} â€“ 65

âˆ´ âˆ x = 115^{o}

**13. Fill in the blanks:**

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

**Solution:-**

If two angles are complementary, then the sum of their measures is 90^{o}.

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

**Solution:-**

If two angles are supplementary, then the sum of their measures is 180^{o}.

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

**Solution:-**

Two angles forming a linear pair are Supplementary.

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

**Solution:-**

If two adjacent angles are supplementary, they form a linear pair.

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

**_____________.**

**Solution:-**

If two lines intersect at a point, then the vertically opposite angles are always 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 __________.**

**Solution:-**

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 Obtuse angles.

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

**(i) Obtuse vertically opposite angles**

**Solution:-**

âˆ AOD and âˆ BOC are obtuse vertically opposite angles in the given figure.

**(ii) Adjacent complementary angles**

**Solution:-**

âˆ EOA and âˆ AOB are adjacent complementary angles in the given figure.

**(iii) Equal supplementary angles**

**Solution:-**

âˆ EOB and EOD are the equal supplementary angles in the given figure.

**(iv) Unequal supplementary angles**

**Solution:-**

âˆ EOA and âˆ EOC are the unequal supplementary angles in the given figure.

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

**Solution:-**

âˆ AOB and âˆ AOE, âˆ AOE and âˆ EOD, âˆ EOD and âˆ COD are the adjacent angles that do not form a linear pair in the given figure.