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

**Ex 5.1 Class 7 Maths Question 1.**

Find the complement of each of the following angles :

**Solution:**

- Complement of the angle 20° = 90° – 20° = 70°
- Complement of the angle 63° = 90° – 63° = 27°
- Complement of the angle 57° = 90° – 57° = 33°

**Ex 5.1 Class 7 Maths 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 measure 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°.

**Ex 5.1 Class 7 Maths Question 3.**

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

(i) 65°, 115°

(ii) 63°, 27°

(iii) 112°, 68°

(iv) 130°, 50°

(v) 45°, 45°

(vi) 80°, 10°

**Solution:
**

**(i)**65°, 115°

∵ 65° + 115° = 180°

∴ The given pair of angles are supplementary.

**(ii)** 63°, 27°

∵ 63° + 27° = 90°

The given pair of angles are complementary.

**(iii)** 112°, 68°

∵ 112° + 68° = 180°

∴ The given pair of angles are supplementary.

**(iv)** 130°, 50°

∵ 130° + 50° = 180°

∴ The given pair of angles are supplementary.

**(v)** 45°, 45°

∵45° + 45° = 90°

∴ The given pair of angles are complementary.

**(vi)** 80°, 10°

∵ 80° + 10° = 90°

∴ The given pair of angles are complementary.

**Ex 5.1 Class 7 Maths Question 4.**

Find the angle which is equal to its complement.

**Solution:**

Let the angle be x°.

Its complement = 90° – x°

According to the question,

x° = 90° – x0

⇒ x° + x° = 90°

⇒ 2x° = 90°

⇒ x° = \(\frac { { 90 }^{ \circ } }{ 3 }\) = 45°

**Ex 5.1 Class 7 Maths Question 5.**

Find the angle which is equal to its supplement.

**Solution:**

Let the angle be x°.

Its supplement = 180° – x°

According to the question,

x° = 180° – x°

⇒ x° + x° = 180°

⇒ 2x° = 180°

⇒ x° = \(\frac { { 180 }^{ \circ } }{ 3 }\) = 90°

Hence, the required angle is 90°.

**Ex 5.1 Class 7 Maths 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.

**Ex 5.1 Class 7 Maths Question 7.**

Can two angles be supplementary if both of them are :

- acute?
- obtuse?
- right?

**Solution:**

- No
- No
- Yes

**Ex 5.1 Class 7 Maths 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°.

**Ex 5.1 Class 7 Maths 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! ∠ 1 is adjacent to ∠ 2.
- No! ∠ AOC is not adjacent to ∠ AOE.
- Yes! ∠ COE and ∠ EOD form a linear pair.
- Yes! ∠ BOD and ∠ DOA are supplementary.
- Yes! ∠ 1 is vertically opposite to ∠ 4.
- The vertically opposite angle of ∠ 5 is ∠ 2 + ∠ 3, i.e., ∠ COB.

**Ex 5.1 Class 7 Maths Question 10.**

Indicate which pairs of angles are :

- Vertically opposite angles.
- Linear pairs.

**Solution:**

- ∠1 and ∠4; ∠5 and ∠2 + ∠3
- ∠4 and ∠5; ∠5 and ∠1

**Ex 5.1 Class 7 Maths Question 11.**

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

**Solution:**

No! ∠ 1 is not adjacent to ∠ 2 because their vertex is not common.

**Ex 5.1 Class 7 Maths Question 12.**

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

**Solution:
**

**Ex 5.1 Class 7 Maths Question 13.**

**Fill in the blanks:**

- If two angles are complementary, then the sum of their measures is __________
- If two angles are supplementary, then the sum of their measures is __________
- Two angles forming a linear pair are __________
- If two adjacent angles are supplementary, they form a __________
- If two lines intersect at a point, then the vertically opposite angles are always __________
- 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:**

- 90°
- 180°
- supplementary
- linear pair
- equal
- obtuse angles

**Ex 5.1 Class 7 Maths 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 do not form a linear pair.

**Solution:**

- ∠ AOD and ∠ BOC
- ∠ EOA and ∠ AOB
- ∠ BOE and ∠ DOE
- ∠ EOC and ∠ EOA
- ∠ AOB and ∠ AOE ; ∠ AOE and ∠ EOD ; ∠ EOD and ∠ DOC.

### Chapter 5 Lines and Angles Exercise 5.2

**Ex 5.2 Class 7 Maths 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.

**Ex 5.2 Class 7 Maths 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.

**Ex 5.2 Class 7 Maths Question 3.**

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

**Solution:
**

**Ex 5.2 Class 7 Maths 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]

**Ex 5.2 Class 7 Maths Question 5.**

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

**(i)** DGC

**(ii)** DEF

**Solution:
**

**Ex 5.2 Class 7 Maths Question 6.**

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

**Solution:
**

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