Contents

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 7 |

Subject |
Maths |

Chapter |
Chapter 5 |

Chapter Name |
Lines and Angles |

Exercise |
Ex 5.1, Ex 5.2. |

Number of Questions Solved |
20 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

### Chapter 5 Lines and Angles Exercise 5.1

**Question 1.**

Find the complement of each of the following angles :

**Solution:**

Since, the sum of the measures of an angle and its complement is 90°, therefore,

- The complement of an angle of measure 20° is the angle of (90°-20°), f.e., 70°.
- The complement of an angle of measure 63° is the angle of (90°-63°), i.e., 27°.
- The complement of an angle of measure 57° is the angle of (90°-57°), i.e., 33°.

**Question 2.**

Find the supplement of each of the following angles :

**Solution:**

Since, the sum of the measures of an angle and its supplement is 180°, therefore,

- The supplement of an angle of measvjre 105° is the angle of (180°-105°), i.e., 75°.
- The supplement of an angle of measure 87° is the angle of (180°-87°), i.e., 93°.
- The supplement of an angle of measure 154° is the angle of (180°-154°), i.e., 26°.

**Question 3.**

Identify which of the following pairs of angles are complementary and which are supplementary :

- 65°, 115°
- 63°, 27°
- 112°, 68°
- 130°, 50°
- 45°, 45°
- 80°, 10°

**Solution:**

- Since, 65°+ 115° = 180°

So, this pair of angles is supplementary. - Since, 63°+ 27° = 90°

So, this pair of angles is complementary. - Since, 112° + 68° = 1800

So, this pair of angles is supplementary. - Since, 130°+50° = 180°

So, this pair of angles is supplementary. - Since, 45°+ 45° = 90°

So, this pair of angles is complementary. - Since, 80°+ 10° = 90°

So, this pair of angles is complementary.

**Question 4.**

Find the angle which is equal to its complement.

**Solution:**

Let the measure of the angle be x°. Then, the measure of its complement is given to be x°.

Since, the sum of the measures of an angle and its complement is 90°, therefore,

x° + x° = 90°

⇒ 2x° = 90°

⇒ x° = 45°

Thus, the required angle is 45°.

**Question 5.**

Find the angle which is equal to its supplement.

**Solution:**

Let the measure of the angle be x°. Then,

measure of its supplement = x°

Since, the sum of the measures of an angle and its supplement is 180°, therefore,

x° + x° = 180°

⇒ 2x° =180°

⇒ x° = 90°

Hence, the required angle is 90°.

**Question 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?

**Solution:**

∠2 will increase with the same measure as the decrease in ∠1.

**Question 7.**

Can two angles be supplementary if both of them are :

- acute?
- obtuse?
- right?

**Solution:**

- No
- No
- Yes

**Question 8.**

An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

**Solution:**

Since, the sum of the measure of ah angle and its complement is 90°.

∴ The complement of an angle of measures 45° + x°, where x > 0 is the angle of [90° – (45° + x°)] = 90° – 45° – x°= 45° – x°.

Clearly, 45° + x° > 45° – x°

Hence, the complement of an angle > 45° is less than 45°.

**Question 9.**

In the adjoining figure

- Is ∠1 adjacent to ∠2 ?
- Is ∠AOC adjacent to ∠AOE?
- Do ∠COE and ∠EOD form a linear pair?
- Are ∠BOD and ∠DOA supplementary?
- Is ∠1 vertically opposite to Z4?
- What is the vertically opposite angle of ∠5

**Solution:**

- Yes
- No
- Yes
- Yes
- Yes
- ∠2 + ∠3 = ∠COB

**Question 10.**

Indicate which pairs of angles are :

- Vertically opposite angles.
- Linear pairs.

**Solution:**

- Pair of vertically opposite angles are ∠1, ∠4; ∠5, ∠2 + ∠3.
- Pair of linear angles are ∠1, ∠5; ∠4, ∠5.

**Question 11.**

In the adjoining figure, is ∠1 adjacent to ∠2? Give reasons.

**Solution:**

∠1 is not adjacent to ∠2 because they have no common vertex.

**Question 12.**

Find the values of the angles x, y and z in each of the following?

**Solution:
**

**Question 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 __________

**Solution:**

**(i)** 90°

**(ii)** 180°

**(iii)** supplementary

**(iv)** linear pair

**(v)** equal

**(vi)** obtuse angles

**Question 14.**

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

- Obtuse vertically opposite angles.
- Adjacent complementary angles.
- Equal supplementary angles.
- Unequal supplementary angles.
- Adjacent angles that do not form a linear pair.

**Solution:**

- Obtuse vertically opposite angles are ∠AOD and ∠BOC.
- Adjacent complementary angles are ∠BOA and ∠AOE.
- Equal supplementary angles are ∠BOE and ∠EOD.
- Unequal supplementary angles are ∠BOA and ∠AOD, ∠BOC and ∠COD, ∠EOA and ∠EOC.
- Adjacent angles that do not form a linear pair are ∠AOB and ∠AOE, ∠AOE and ∠EOD; ∠EOD and ∠COD.

### Chapter 5 Lines and Angles Exercise 5.2

**Question 1.**

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

**Solution:**

**(i)** Corresponding angle property.

**(ii)** Alternate interior angle property.

**(iii)** Interior angles on the same side of the transversal are supplementary.

**Question 2.**

In the adjoining figure, identify :

- the pairs of corresponding angles.
- the pairs of alternate interior angles.
- the pairs of interior angles on the same side of the transversal.
- the vertically opposite angles

**Solution:**

- ∠1, ∠5; ∠2, ∠6; ∠3, ∠7 and ∠4, ∠8 are four pairs of corresponding angles.
- ∠2, ∠8 and ∠3, ∠5 are two pairs of alternate interior angles.
- ∠2, ∠5 and ∠3, ∠8 are two pairs of interior angles on the same side of the transversal.
- ∠1, ∠3; ∠2, ∠4; ∠5, ∠7 and ∠6, ∠8 are four pairs of vertically opposite angles.

**Question 3.**

In the adjoining figure p || q. Find the unknown angles

**Solution:
**

**Question 4.**

Find the value of x in each of the following figures if l || m :

**Solution:**

**(i)** Since, l || m and t is a transversal.

∴ ∠x = (180° – 110°) = 70° [Corresponding angles, Linear pair]

**(ii)** if l || m and a is a transversal.

Then, ∠x = 1000 [Corresponding angles]

**Question 5.**

In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find

**(i)** DGC

**(ii)** DEF

**Solution:
**

**Question 6.**

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

**Solution:
**

We hope the NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles help you. If you have any query regarding NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest.

## Leave a Reply