NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1.

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 |
14 |

Category |
NCERT Solutions |

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

- Supplement of the angle 105° = 180° – 105° = 75°
- Supplement of the angle 87° = 180° – 87° = 93°
- Supplement of the angle 154° = 180° – 154° = 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 are supplementary. - Since, 63°+ 27° = 90°

So, this pair of angles are complementary. - Since, 112° + 68° = 180°

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

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

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

So, this pair of angles are 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,

a 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 as much as ∠ 1 decreases.

**Question 7.**

Can two angles be supplementary if both of them are:

- acute?
- obtuse?
- right?

**Solution:**

- No! two acute angles cannot be a supplement.
- No! Two obtuse angles cannot be supplementary.
- Yes! Two right angles are always supplementary.

**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 ∠ 4?
- 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.

**Question 10.**

Indicate which pairs of angles are:

- Vertically opposite angles.
- Linear pairs.

**Solution:**

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

**Question 11.**

In the following 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:

- 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

**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.

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