RD Sharma Solutions (Part - 1) - Ex-14.1, Lines and Angles, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

Write down each pair of adjacent angles shown in Fig.

Answer 1:

Adjacent angles are the angles that have a common vertex and a common arm.
Following are the adjacent angles in the given figure:

∠DOC and ∠BOC
∠COB and ∠BOA

Question 2:

In Fig., name all the pairs of adjacent angles.

Answer 2:

In figure (i), the adjacent angles are:

∠EBA and∠ABC
∠ACB and ∠BCF
∠BAC and ∠CAD

In figure (ii), the adjacent angles are:

∠∠BAD and ∠∠DAC
∠∠BDA and ∠∠CDA

Question 3:

In figure, write down: (i) each linear pair (ii) each pair of vertically opposite angles.

Answer 3:

(i) 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) Two angles formed by two intersecting lines having no common arms are called vertically opposite angles.
∠1 and ∠4
∠2 and ∠3
∠5 and ∠8
∠6 and ∠7

Question 4:

Are the angles 1 and 2 given in Fig. adjacent angles?

Answer 4:

No, because they have no common vertex.

Question 5:

Find the complement of each of the following angles:
 (i) 35°
 (ii) 72°
 (iii) 45°
 (iv) 85°

Answer 5:

Two angles are called complementary angles if the sum of those angles is 90°.

Complementary angles of the following angles are:

(i) 90°−35°=55°
(ii) 90°−72°=18°
(iii) 90°−45°=45°
(iv) 90°−85°=5°

Question 6:

Find the supplement of each of the following angles:
 (i) 70°
 (ii) 120°
 (iii) 135°
 (iv) 90°

Answer 6:

Two angles are called supplementary angles if the sum of those angles is 180°.
Supplementary angles of the following angles are:

(i) 180° − 70° = 110°
(ii) 180° − 120° = 60°
(iii) 180° − 135° = 45°
(iv) 180° − 90° = 90°

Question 7:

Identify the complementary and supplementary pairs of angles from the following pairs:
 (i) 25°, 65°
 (ii) 120°, 60°
 (iii) 63°, 27°
 (iv) 100°, 80°

Answer 7:

Since
(i) 25°+65°=90° , therefore this is complementary pair of angle.
(ii) 120°+ 60°= 180°, therefore this is supplementary pair of angle.
(iii) 63°+27°= 90°, therefore this is complementary pair of angle.
(iv) 100°+ 80°= 180° , therefore this is supplementary pair of angle.

Therefore, (i) and (iii) are the pairs of complementary angles and (ii) and (iv) are the pairs of supplementary angles.

Question 8:

Can two angles be supplementary, if both of them be
 (i) obtuse?
 (ii) right?
 (iii) acute?

Answer 8:

(i) No, two obtuse angles cannot be supplementary.
(ii) Yes, two right angles can be supplementary. (∵∠90°+∠90°=∠180°)
(iii) No, two acute angles cannot be supplementary.

Question 9:

Name the four pairs of supplementary angles shown in Fig.

Answer 9:

Following are the supplementary angles:
∠AOC and ∠COB
∠BOC and ∠DOB
∠BOD and ∠DOA
∠AOC and ∠DOA

Question 10:

In Fig., A, B, C are collinear points and ∠DBA = ∠EBA.

(i) Name two linear pairs
 (ii) Name two pairs of supplementary angles.

Answer 10:

(i) Linear pairs:
∠ABD and ∠DBC
∠ABE and ∠EBC

Because every linear pair forms supplementary angles, these angles are:
∠ABD and ∠DBC
∠ABE and ∠EBC

Question 11:

If two supplementary angles have equal measure, what is the measure of each angle?

Answer 11:

Let x and y be two supplementary angles that are equal.
∠x=∠y
According to the question,
∠x+∠y=180°
⇒∠x+∠x=180°
⇒2∠x=180°

Question 12:

If the complement of an angle is 28°, then find the supplement of the angle.

Answer 12:

Let x be the complement of the given angle 28°28°.
∴ ∠x+28°=90°
⇒∠x=90°−28°=62°

So, supplement of the angle = 180°−62°=118°180°-62°=118°

Question 13:

In Fig. 19, name each linear pair and each pair of vertically opposite angles:

Answer 13:

Two adjacent angles are said to form a linear pair of angles if their non-common arms are two opposite rays.

∠1 and ∠2
∠2 and ∠3
∠3 and ∠4
∠1 and ∠4
∠5 and ∠6
∠6 and ∠7
∠7 and ∠8
∠8 and ∠5
∠9 and ∠10
∠10 and ∠11
∠11 and ∠12
∠12 and ∠9

Two angles formed by two intersecting lines having no common arms are called vertically opposite angles.
∠1 and ∠3
∠4 and ∠2
∠5 and ∠7
∠6 and ∠8
∠9 and ∠11
∠10 and ∠12

Question 14:

In Fig., OE is the bisector of ∠BOD. If ∠1 = 70°, find the magnitudes of ∠2, ∠3 and ∠4.

Answer 14:

Since OE is the bisector of ∠∠BOD,
∴∠DOE=∠EOB

∠2+∠1+∠EOB=180°                 (Linear Pair)
∠2+2∠1=180°              (∠1=∠EOB)
⇒∠2=180°−2∠1=180°−2×70°=180°−140°=40°
∠4=∠2=40°                (Vertically opposite angles)
∠3=∠DOB=∠1+∠EOB=70°+70°=140°            [∠3=∠DOB (Vertically opposite angles)