Exercise 5.1
"Lines and Angles" Chapter 5 - Introduction - NCERT Class 7th Maths Solutions
Q 1, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 1
Find the complement of each of the following angles:
The sum of the measures of complementary angles is 90°.
(i) 20°
Complement = 90° - 20°
= 70°
(ii) 63°
Complement = 90° - 63°
= 27°
(iii) 57°
Complement = 90° - 57°
= 33°
Q 2, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 2
Find the supplement of each of the following angles:
The sum of the measures of supplementary angles is 180°
(i) 105°
Supplement = 180° - 105°
= 75°
(ii) 87°
Supplement = 180° - 87°
= 93°
(iii) 154°
Supplement = 180° — 154°
= 26°
Q 3, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 3
Identify which of the following pairs of angles are complementary and which are supplementary.
NOTE : The sum of the measures of complementary angles is 90° and that of supplementary
angles is 180°.
(i) 65°,115°
Sol :
Sum of the measures of these angles = 65° +115° = 180°
∴These angles are supplementary angles.
(ii) 63°, 27°
Sol :
Sum of the measures of these angles = 63° + 27° = 90°
∴These angles are complementary angles.
(iii) 112°, 68°
Sol :
Sum of the measures of these angles = 112° + 68° = 180°
∴These angles are supplementary angles.
(iv) 130°, 50°
Sol :
Sum of the measures of these angles = 130° + 50° = 180°
∴These angles are supplementary angles.
(v) 45°, 45°
Sol :
Sum of the measures of these angles = 45° + 45° = 90°
∴These angles are complementary angles.
(vi) 80°, 10°
Sol :
Sum of the measures of these angles = 80° + 10° = 90°
∴These angles are complementary angles.
Q 4, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 4
Find the angles which is equal to its complement.
Sol :
Let the angle be x
Complement of this angle is also x
The sum of the measures of a complementary angle pair is 90°
x + x = 90°
2x= 90°
x $\dfrac{90°}{2}$
x = 45°
Q 5, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 5
Find the angles which is equal to its supplement.
Sol :
Let the angle be x
Supplement of this angle is also x
The sum of the measures of a supplementary angle pair is 180°
x + x = 180°
2x = 180°
x = 90°
Q 6, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
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.
Sol :
∠1 and ∠2 are supplementary angles.
If ∠1 is reduced, then ∠2 should be increased by the same measure so that this angle pair remains supplementary
Q 7, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 7
Can two angles be supplementary if both of them are:
(i) Acute ? (ii) Obtuse ? (iii) Right ?
Sol :
(i) No. Acute angle is always lesser than 90°. It can be observed that two angles, even of 89°, cannot add up to 180°. Therefore, two acute angles cannot be in a supplementary angle pair.
(ii) No. Obtuse angle is always greater than 90°. It can be observed that two angles, even of 91°, will always add up to more than 180°. Therefore, two obtuse angles
(iii) Yes. Right angles are of 90° and 90° + 90° = 180° . Therefore, two right angles form a supplementary angle pair together.
Q 8, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 8
An angle is greater than 45°. ls its complementary angle greater than 45° or equal to 45° or less than 45° ?
Sol :
Let A and B are two angles making a complementary angle pair and A is greater than 45°
A + B = 90°
B = 90° - A
Therefore, 8 will be lesser than 45°
Q 9, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 9
In the adjoining figure:
(i) Is ∠1 adjacent to ∠2 ?
(ii) Is ∠A0C adjacent to ∠AOE ?
(iii) Do ∠COE and ∠E0D 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 ?
Sol :
(i) Yes, Since they have a common vertex O and also a common arm OC. Also, their non-common arms, OA and OE , are on either side of the common arm.
(ii) No, They have a common vertex O and also a common arm OA. However, their non-common arms, OC and OE, are on the same side of the common arm. Therefore, these are not adjacent to each other.
(iii) Yes, Since they have a common vertex O and a common arm OE. Also, their non-common arms, OC and OD, are opposite rays.
(iv) Yes, Since ∠BOD and ∠DOA have a common vertex O and their non-common arms are opposite to each other.
(v) Yes, Since these are formed due to the intersection of two straight lines (AB and CD )
(vi) ∠COB is the vertically opposite angle of ∠5 as these are formed due to the intersection of two straight lines, AB and CD.
Q 10, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 10
Indicate which pairs of angles are:
(i) Vertically opposite angles. (ii) Linear pairs.
Sol :
(i) ∠1 and ∠4, ∠5 and ∠2 +∠3 are vertically opposite angles as these are formed due to the intersection of two straight lines.
(ii) ∠1 and ∠5, ∠5 and ∠4 are linear pairs as these have a common vertex and also have non-common arms opposite to each other , also they have a common vertex .
QUESTION 11
Sol :
∠1 and ∠2 are not adjacent angles because their vertex is not common.
Q 12, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 12
Find the value of the angles x , y, and z in each of the following:
(i)
Sol :
Since ∠x and ∠55° are vertically opposite angles,
∠x = ∠55°
∠x + ∠y = 180° (Linear pair)
∠55° + ∠y = 180° (∠x = ∠55°)
∠y = 180° - ∠55°
∠y = 125°
∠y = ∠z (Vertically opposite angles)
∠z =125°
(ii)
Sol :
∠z = 40° (Vertically opposite angles)
∠y+ ∠z= 180° (Linear pair)
∠y = 180° - 40°
∠y = 140°
40° + ∠x+ 25° = 180° (Angles on a straight line)
65° + ∠x = 180°
∠x = 180° - 65°
∠x = 115°
Q 13, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 13
Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is 90° .
(ii) If two angles are supplementary, then the sum of their measures is 180° .
(iii) Two angles forming a linear pair are supplementary .
(iv) If two adjacent angles are supplementary, they form a linear pair .
(v) If two lines intersect at a point, then the vertically opposite angles are always equal .
(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 obtuse angle .
Q 14, Ex 5.1 - Lines and Angles - Chapter 5 - Maths Class 7th - NCERT
QUESTION 14
In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
Sol :
∠AOD , ∠BOC
(ii) Adjacent complementary angles
Sol :
∠EOA , ∠AOB
(iii) Equal supplementary angles
Sol :
∠EOB , ∠EOD
(iv) Unequal supplementary angles
Sol :
∠EOA , ∠EOC
(v) Adjacent angles that do not form a linear pair
Sol :
∠AOB and ∠AOE , ∠AOE and ∠EOD , ∠EOD and ∠COD
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