Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Lines & Angles (Exercise 14.1)
Lines & Angles (Exercise 14.1) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download
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Page 1
1. Write down each pair of adjacent angles shown in fig. 13.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in given figure are:
?DOC and ?BOC
?COB and ?BOA
2. In Fig. 14, name all the pairs of adjacent angles.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles.
In fig (i), the adjacent angles are
?EBA and ?ABC
?ACB and ?BCF
?BAC and ?CAD
In fig (ii), the adjacent angles are
Page 2
1. Write down each pair of adjacent angles shown in fig. 13.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in given figure are:
?DOC and ?BOC
?COB and ?BOA
2. In Fig. 14, name all the pairs of adjacent angles.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles.
In fig (i), the adjacent angles are
?EBA and ?ABC
?ACB and ?BCF
?BAC and ?CAD
In fig (ii), the adjacent angles are
?BAD and ?DAC
?BDA and ?CDA
3. In fig. 15, write down
(i) Each linear pair
(ii) Each pair of vertically opposite angles.
Solution:
(i) The two adjacent angles are said to form a linear pair of angles if their non – common
arms are two opposite rays.
?1 and ?3
?1 and ?2
?4 and ?3
?4 and ?2
?5 and ?6
?5 and ?7
?6 and ?8
?7 and ?8
(ii) The two angles formed by two intersecting lines and have no common arms are
called vertically opposite angles.
?1 and ?4
?2 and ?3
?5 and ?8
?6 and ?7
4. Are the angles 1 and 2 given in Fig. 16 adjacent angles?
Page 3
1. Write down each pair of adjacent angles shown in fig. 13.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in given figure are:
?DOC and ?BOC
?COB and ?BOA
2. In Fig. 14, name all the pairs of adjacent angles.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles.
In fig (i), the adjacent angles are
?EBA and ?ABC
?ACB and ?BCF
?BAC and ?CAD
In fig (ii), the adjacent angles are
?BAD and ?DAC
?BDA and ?CDA
3. In fig. 15, write down
(i) Each linear pair
(ii) Each pair of vertically opposite angles.
Solution:
(i) The two adjacent angles are said to form a linear pair of angles if their non – common
arms are two opposite rays.
?1 and ?3
?1 and ?2
?4 and ?3
?4 and ?2
?5 and ?6
?5 and ?7
?6 and ?8
?7 and ?8
(ii) The two angles formed by two intersecting lines and have no common arms are
called vertically opposite angles.
?1 and ?4
?2 and ?3
?5 and ?8
?6 and ?7
4. Are the angles 1 and 2 given in Fig. 16 adjacent angles?
Solution:
No, because they don’t have common vertex.
5. Find the complement of each of the following angles:
(i) 35
o
(ii) 72
o
(iii) 45
o
(iv) 85
o
Solution:
(i) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 35
o
= 55
o
(ii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
0
– 72
o
= 18
o
(iii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 45
o
= 45
o
(iv) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 85
o
= 5
o
6. Find the supplement of each of the following angles:
(i) 70
o
(ii) 120
o
(iii) 135
o
(iv) 90
o
Page 4
1. Write down each pair of adjacent angles shown in fig. 13.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in given figure are:
?DOC and ?BOC
?COB and ?BOA
2. In Fig. 14, name all the pairs of adjacent angles.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles.
In fig (i), the adjacent angles are
?EBA and ?ABC
?ACB and ?BCF
?BAC and ?CAD
In fig (ii), the adjacent angles are
?BAD and ?DAC
?BDA and ?CDA
3. In fig. 15, write down
(i) Each linear pair
(ii) Each pair of vertically opposite angles.
Solution:
(i) The two adjacent angles are said to form a linear pair of angles if their non – common
arms are two opposite rays.
?1 and ?3
?1 and ?2
?4 and ?3
?4 and ?2
?5 and ?6
?5 and ?7
?6 and ?8
?7 and ?8
(ii) The two angles formed by two intersecting lines and have no common arms are
called vertically opposite angles.
?1 and ?4
?2 and ?3
?5 and ?8
?6 and ?7
4. Are the angles 1 and 2 given in Fig. 16 adjacent angles?
Solution:
No, because they don’t have common vertex.
5. Find the complement of each of the following angles:
(i) 35
o
(ii) 72
o
(iii) 45
o
(iv) 85
o
Solution:
(i) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 35
o
= 55
o
(ii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
0
– 72
o
= 18
o
(iii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 45
o
= 45
o
(iv) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 85
o
= 5
o
6. Find the supplement of each of the following angles:
(i) 70
o
(ii) 120
o
(iii) 135
o
(iv) 90
o
Solution:
(i) The two angles are said to be supplementary angles if the sum of those angles is 180
o
Therefore supplementary angle for the given angle is
180
o
– 70
o
= 110
o
(ii) The two angles are said to be supplementary angles if the sum of those angles is 180
o
Therefore supplementary angle for the given angle is
180
o
– 120
o
= 60
o
(iii) The two angles are said to be supplementary angles if the sum of those angles is
180
o
Therefore supplementary angle for the given angle is
180
o
– 135
o
= 45
o
(iv) The two angles are said to be supplementary angles if the sum of those angles is
180
o
Therefore supplementary angle for the given angle is
180
o
– 90
o
= 90
o
7. Identify the complementary and supplementary pairs of angles from the following
pairs:
(i) 25
o
, 65
o
(ii) 120
o
, 60
o
(iii) 63
o
, 27
o
(iv) 100
o
, 80
o
Solution:
(i) 25
o
+ 65
o
= 90
o
so, this is a complementary pair of angle.
(ii) 120
o
+ 60
o
= 180
o
so, this is a supplementary pair of angle.
(iii) 63
o
+ 27
o
= 90
o
so, this is a complementary pair of angle.
(iv) 100
o
+ 80
o
= 180
o
so, this is a supplementary pair of angle.
8. Can two obtuse angles be supplementary, if both of them be
(i) Obtuse?
(ii) Right?
Page 5
1. Write down each pair of adjacent angles shown in fig. 13.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles
Therefore the adjacent angles in given figure are:
?DOC and ?BOC
?COB and ?BOA
2. In Fig. 14, name all the pairs of adjacent angles.
Solution:
The angles that have common vertex and a common arm are known as adjacent angles.
In fig (i), the adjacent angles are
?EBA and ?ABC
?ACB and ?BCF
?BAC and ?CAD
In fig (ii), the adjacent angles are
?BAD and ?DAC
?BDA and ?CDA
3. In fig. 15, write down
(i) Each linear pair
(ii) Each pair of vertically opposite angles.
Solution:
(i) The two adjacent angles are said to form a linear pair of angles if their non – common
arms are two opposite rays.
?1 and ?3
?1 and ?2
?4 and ?3
?4 and ?2
?5 and ?6
?5 and ?7
?6 and ?8
?7 and ?8
(ii) The two angles formed by two intersecting lines and have no common arms are
called vertically opposite angles.
?1 and ?4
?2 and ?3
?5 and ?8
?6 and ?7
4. Are the angles 1 and 2 given in Fig. 16 adjacent angles?
Solution:
No, because they don’t have common vertex.
5. Find the complement of each of the following angles:
(i) 35
o
(ii) 72
o
(iii) 45
o
(iv) 85
o
Solution:
(i) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 35
o
= 55
o
(ii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
0
– 72
o
= 18
o
(iii) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 45
o
= 45
o
(iv) The two angles are said to be complementary angles if the sum of those angles is 90
o
Complementary angle for given angle is
90
o
– 85
o
= 5
o
6. Find the supplement of each of the following angles:
(i) 70
o
(ii) 120
o
(iii) 135
o
(iv) 90
o
Solution:
(i) The two angles are said to be supplementary angles if the sum of those angles is 180
o
Therefore supplementary angle for the given angle is
180
o
– 70
o
= 110
o
(ii) The two angles are said to be supplementary angles if the sum of those angles is 180
o
Therefore supplementary angle for the given angle is
180
o
– 120
o
= 60
o
(iii) The two angles are said to be supplementary angles if the sum of those angles is
180
o
Therefore supplementary angle for the given angle is
180
o
– 135
o
= 45
o
(iv) The two angles are said to be supplementary angles if the sum of those angles is
180
o
Therefore supplementary angle for the given angle is
180
o
– 90
o
= 90
o
7. Identify the complementary and supplementary pairs of angles from the following
pairs:
(i) 25
o
, 65
o
(ii) 120
o
, 60
o
(iii) 63
o
, 27
o
(iv) 100
o
, 80
o
Solution:
(i) 25
o
+ 65
o
= 90
o
so, this is a complementary pair of angle.
(ii) 120
o
+ 60
o
= 180
o
so, this is a supplementary pair of angle.
(iii) 63
o
+ 27
o
= 90
o
so, this is a complementary pair of angle.
(iv) 100
o
+ 80
o
= 180
o
so, this is a supplementary pair of angle.
8. Can two obtuse angles be supplementary, if both of them be
(i) Obtuse?
(ii) Right?
(iii) Acute?
Solution:
(i) No, two obtuse angles cannot be supplementary
Because, the sum of two angles is greater than 90
o
so their sum will be greater than
180
o
(ii) Yes, two right angles can be supplementary
Because, 90
o
+ 90
o
= 180
o
(iii) No, two acute angle cannot be supplementary
Because, the sum of two angles is less than 90
o
so their sum will also be less than 90
o
9. Name the four pairs of supplementary angles shown in Fig.17.
Solution:
The two angles are said to be supplementary angles if the sum of those angles is 180
o
The supplementary angles are
?AOC and ?COB
?BOC and ?DOB
?BOD and ?DOA
?AOC and ?DOA
10. In Fig. 18, A, B, C are collinear points and ?DBA = ?EBA.
(i) Name two linear pairs.
(ii) Name two pairs of supplementary angles.
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FAQs on Lines & Angles (Exercise 14.1) RD Sharma Solutions - Mathematics (Maths) Class 7
| 1. How do you find the measure of an angle using a protractor? |  |
Ans. To find the measure of an angle using a protractor, place the center of the protractor on the vertex of the angle. Align one side of the angle with the baseline of the protractor. Read the measure where the other side of the angle intersects with the protractor scale.
| 2. What is the difference between a straight angle and a reflex angle? | |
Ans. A straight angle measures exactly 180 degrees and forms a straight line. On the other hand, a reflex angle measures more than 180 degrees and less than 360 degrees. It forms a rotation greater than a straight angle but less than a full circle.
| 3. How can you identify corresponding angles? | |
Ans. Corresponding angles are formed when two parallel lines are intersected by a transversal. To identify corresponding angles, look for pairs of angles that are in the same relative position with respect to the transversal. These angles will have the same measure.
| 4. What is an alternate interior angle? | |
Ans. An alternate interior angle is formed when two parallel lines are intersected by a transversal. These angles are located on the inside of the parallel lines, but on opposite sides of the transversal. Alternate interior angles are congruent, meaning they have the same measure.
| 5. How can you determine if two lines are perpendicular? | |
Ans. Two lines are perpendicular if they intersect at a right angle, which measures 90 degrees. To determine if two lines are perpendicular, you can check if the slopes of the lines are negative reciprocals of each other. If the product of the slopes is -1, then the lines are perpendicular.
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Oct 24, 2024 Last updated |
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