Students can Download Chapter 5 Lines and Angles Ex 5.1, Question and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths, Karnataka State Board Solutions help you to revise complete Syllabus and score more marks in your examinations.

## Karnataka State Syllabus Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

Question 1.

Find the complement of each of the following angles :

i) The complement of 70°

Solution:

The complement of the angle 20° = 90° – 20° = 70°

ii)

The complement of the angle 63° = 90° – 63° = 27°

iii)

The complement of the angle 57° = 90° – 57° = 33°

Question 2.

Find the supplement of each of the following angles :

Solution:

i)

The supplement of the angle 105°= 180° – 105° = 75°

ii)

The supplement of the angle 87°= 180° – 87° = 93°

iii) <

The supplement of the angle 154°= 180° – 154° = 26°

Question 3.

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

i) 65°, 115°

65° + 115° = 180°

∴ This pair is supplementary angles.

ii) 63°, 27°

63°+ 27° = 90°

∴ This pair is complementary angles.

iii) 112°, 68°

112°+68°= 1800

∴ This pair is supplementary angles.

iv) 130°, 50°

130° + 50° = 180°

∴ This pair is supplementary angles.

v) 45°, 45°

45° + 45° = 90°

∴ This pair is complementary angles.

vi) 80°, 10°

80°+ 10° = 90°

This pair is complementary angles.

Question 4.

Find the angle which is equal to its complement.

Solution:

Let one of the complement angle be x°

Its complement be = 90° – x

∴ According to the question

x° = 90° – x°

x° + x° = 90°

2x° = 90°

x = 90/2 = 45°

Question 5.

Find the angle which is equal to its supplement.

Solution:

Let one of supplement be x°

Another supplement be = 180° – x°

According to the question = x° = 180° – x°

x° + x° = 180°

2x° = 180°

x° = 180/2 = 90°

Question 6.

In the given figure, ∠1 and ∠2 are supplementary angles.

Solution:

If ∠1 is decreased, what changes should take place in ∠2 so that both the angles still remain supplementary?

If ∠1 is decreased the ∠2 will be increased.

Question 7.

Can two angles be supplementary if both of them are :

i) acute?

No, two acute angles cannot be supplementary. [∵ acute angles is ∠90°]

ii) obtuse?

No, two obtuse angles cannot be supplementary. [∵ obtuse angles is ∠90°].

iii) right?

Yes, Two right angles always supplementary. [∵ right angles is = 90°].

Question 8.

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

Solution:

If an angle is greater than 45° then its complement should be less than 45°.

Question 9.

In the adjoining figure:

i) Is ∠1 adjacent to ∠2?

Yes, ∠1 is adjacent to ∠2

ii) Is ∠AOC adjacent to ∠AOE?

No, ∠AOC is not adjacent to ∠AOE.

iii) Do ∠COE and ∠EOD form a linear pair?

Yes, ∠COE and ∠EOD are linear pairs.

iv) are ∠BOD and ∠DO A supplementary?

Yes, ∠BOD and ∠DOA are supplementary.

v) Is ∠1 vertically opposite to ∠4?

Yes, ∠1 is vertically opposite to ∠4.

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

The vertically opposite angle of ∠5 is ∠2 + ∠3 ie., ∠COB.

∠COE + ∠EOB = ∠COB

Question 10.

Indicate which pairs of angles are :

i) Vertically opposite angles.

Vertically opposite angles are

∠1 and ∠4

∠5 and ∠2 + ∠3

ii) Linear pairs

Linear pairs

∠5 and ∠1

∠4 and ∠5

Question 11.

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

Solution:

∠1 is not adjacent to ∠2 because their vertex is not common.

Question 12.

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

Solution:

Given < = 55°

∠x = 55° (∵ vertically opposite angles)

∠y = 180° – 55° = 125° (∵ linear pair)

∠z = ∠y = 125°(∵ vertically opposite angles)

ii)

Given

∠AOC = 40°

∠EOB = 25° .

AOB is a straight angIe (∵ AOB is st line)

∠AOB = ∠AOC + ∠EOB

180° = 40° + ∠COE + 25°

180° = 65°+ ∠COE

∴ ∠COE = 180° – 65° = 115°

∠y + ∠z = 180°

∠z = 40° (∵ vertically opposite angles)

∴ y = 180° – 40° = 140°

Question 13.

Fill in the blanks :

- If two angles are complementary, then the sum of their measures is
__90°__ - If two angles are supplementary, then the sum of their measures is
__180°__ - Two angles forming a linear pair are
__supplementary__ - If two adjacent angles are supplementary, they form a
__linear pair__ - If two lines intersect at a point, then the vertically opposite angles are always
__equal__ - 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.__

Question 14.

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

Solution:

i) Obtuse vertically opposite angles

∠AOD and ∠BOC

ii) Adjacent complementary angles

∠BOA and ∠AOE

iii) Equal supplementary angles

∠BOE and ∠EOD

iv) Unequal supplementary angles

∠AOE and ∠EOC

v) Adjacent angles that do not form a linear pair

∠AOB and ∠AOE, ∠AOE and ∠EOD and ∠EOD and ∠COD