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Toggle**NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.1** has total fourteen question to practice. Ex 5.1 class 7 is basically about acute, obtuse and Right angle figure in which students need to find required angles. **Class 7 maths chapter 5 exercise 5.1** is given below.

## NCERT Solution For Class Class 7, Maths, Lines And Angles, Exercise 5.1

## Exercise 5.1, Class 7

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

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

∴ Complementary angle = 90^{0} – Given angle

(i) Complement of 63^{0} = 90^{0} – 63^{0} = 27^{0}

(ii) Complement of 20^{0} = 90^{0} – 20^{0} = 70^{0}

(iii) Complement of 57^{0} = 90^{0} – 57^{0} = 33^{0}

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

** **

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

∴ Supplementary angle = 180^{0} – Given angle

(i) Supplement of 105^{0} = 180^{0} – 105^{0} = 75^{0}

(ii) Supplement of 87^{0} = 180^{0} – 87^{0} = 93^{0}

(iii) Supplement of 154^{0} = 180^{0} – 154^{0} = 26^{0}

**Q.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, 10**

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

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

(i) 65°+ 115° = 180° [supplementary angles]

(ii) 63°+ 27° = 90° [Complementary angles]

(iii) 112^{o}+ 68° =180° [supplementary angles]

(iv) 130°+ 50° = 180° [supplementary angles]

(v) 45^{0} + 45^{0} = 90^{0} [Complementary angles]

(vi) 80°+10° =90° [Complementary angles]

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

**Ans: **Let the measure of the required angle = x.

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

Then,

∴ x + x = 90^{o}

⟹ 2x = 90^{o}

⟹ $x=\frac{{{90}^{0}}}{2}$

⟹ x = 45^{o}

Hence, 45^{o} is equal to its complement.

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

**Ans: **Let the measure of the required angle = x.

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

Then,

∴ x + x = 180^{o}

⟹ 2x = 180^{o}

⟹ $x=\frac{{{180}^{0}}}{2}$

⟹ x = 90^{o}

Hence, 90^{o} is equal to its supplement.

**Q.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.**

**Ans: **According to question, ∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 will increase by the same value. So, that both the angles still remain supplementary.

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

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

**Ans: ****(i) Acute: **No, Because, their sum will be always less than 90^{o}.

**(ii) Obtuse: **No, Because, their sum will be always more than 180^{o}.

**(iii) Right: **Yes. Because, their sum will be always 180^{o}.

∴ 90^{o }+ 90^{o} = 180

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

**Ans: **Let us assume the complementary angles be x and y,

We know that, sum of measures of complementary angles are 90^{o}.

Then,

⟹ x + y = 90^{o}

According to question, x > 45^{o}

Adding y on both the sides,

⟹ x + y > 45^{o }+ y

⟹ 90^{o} > 45^{o }+ y

⟹ 90^{o} – 45^{o} > y

⟹ y < 45^{o}

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

**Q.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?**

** ****Ans: ****(i) Is ****∠****1 adjacent to ****∠****2?**

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) Is ****∠****AOC adjacent to ****∠****AOE?**

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 ****∠****COE and ****∠****EOD form a linear pair?**

Yes, they form linear pair.

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

Yes, they are supplementary.

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

Yes, they are vertically opposite angles.

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

Vertically opposite angles of ∠5 is ∠COB.

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

**Ans: ****(i) Vertically opposite angles: **∠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) Linear pairs: **∠1 and ∠5, ∠5 and ∠4 as these are having a common vertex and also having non-common arms opposite to each other.

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

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

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

** **

**Ans:**

**(i) **∠x = 55^{o} [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}

**Thus, **∠x = 55^{o}, ∠y = 125^{o}, and ∠z = 125^{o}.

** **

**(ii) **∠z = 40^{o} [Vertically opposite angles]

∠y + ∠z = 180^{o} [Linear pair]

⟹ ∠y + 40^{o} = 180^{o}

⟹ ∠y = 180^{o} – 40^{o}

⟹ ∠y = 140^{o}

Then, 40^{0} + ∠x + 25^{0} = 180^{o} [Angles on straight line]

⟹ 65^{0} + ∠x = 180^{o}

⟹ ∠x = 180^{o} – 65^{0}

∴ ∠x = 115^{o}

**Thus, **∠x = 115^{o}, ∠y = 140^{o}, and ∠z = 40^{o}.

**Q.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 __________.**

**Ans: ****(i) **90^{o}** (ii)** 180^{o}** (iii) **Supplementary** (iv) **linear pair** (v)** equal** (vi)** Obtuse angles

**Q.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**

**Ans:**

**(i) Obtuse vertically opposite angles**

Obtuse vertically opposite angles means greater than 90^{0} and equal. So, ∠AOD and ∠BOC are obtuse vertically opposite angles.

** **

**(ii) Adjacent complementary angles**

Adjacent complementary angles means angles have common vertex, common arm,

non-common arms are on either side of common arm and sum of angles is 90^{0}.So, ∠EOA and ∠AOB are adjacent complementary angles.

** **

**(iii) Equal supplementary angles**

Equal supplementary angles means sum of angles is 180° and supplement angles are

equal.so, ∠EOB and EOD are the equal supplementary angles.

** **

**(iv) Unequal supplementary angles**

Unequal supplementary angles means sum of angles is 180° and supplement angles

are unequal. So, ∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

** **

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

Adjacent angles that do not form a linear pair mean, angles have common ray but the

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