RD Sharma Solutions (Part - 2) - Ex-14.1, Lines and Angles, Class 7, Math | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 15:

One of the angles forming a linear pair is a right angle. What can you say about its other angle?

Answer 15:

One angle of a linear pair is the right angle, i.e., 90°.
∴ The other angle = 180°​ - 90° = 90​°

Question 16:

One of the angles forming a linear pair is an obtuse angle. What kind of angle is the other?

Answer 16:

If one of the angles of a linear pair is obtuse, then the other angle should be acute; only then can their sum be 180°.

Question 17:

One of the angles forming a linear pair is an acute angle. What kind of angle is the other?

Answer 17:

In a linear pair, if one angle is acute, then the other angle should be obtuse. Only then their sum can be 180°.

Question 18:

Can two acute angles form a linear pair?

Answer 18:

No, two acute angles cannot form a linear pair because their sum is always less than 180°.

Question 19:

If the supplement of an angle is 65°; then find its complement.

Answer 19:

Let x be the required angle.
Then, we have: 
x + 65° = 180°
⇒⇒x = 180° - 65° = 115°

The complement of angle x cannot be determined.

Question 20:

Find the value of x in each of the following figures.

Answer 20:

(i)
Since ∠BOA+∠BOC=180°                  (Linear pair)
∴ ∠x=180°−∠BOA=180°−60°=120°

(ii)
Since ∠QOP+∠QOR=180°         (Linear pair)

∴2x+3x=180°

⇒5x=180°

(v)
2x°+x°+2x°+3x°=180°⇒8x=180

(vi)
3x°=105°

Question 21:

In Fig. 22, it being given that ∠1 = 65°, find all other angles.

Answer 21:

∠1=∠3∠1=∠3          (Vertically opposite angles)
∴∠3=65°∴∠3=65°
Since ∠1+∠2=180°       (Linear pair)
∴∠2=180°−65°=115°
∠2=∠4         (Vertically opposite angles)
∴∠4=∠2=115° and ∠3=65°

Question 22:

In Fig., OA and OB are opposite rays:

(i) If x = 25°, what is the value of y?
(ii) If y = 35°, what is the value of x?

Answer 22:

∠AOC + ∠BOC = 180°                   (Linear pair)
⇒(2y+5)+3x=180°
⇒3x+2y=175°

i) If x = 25°, then
3×25°+2y=175°

⇒75°+2y=175°
⇒2y=175°−75°=100°

(ii) If y = 35°, then
3x+2×35°=175°
⇒3x+70°=175°
⇒3x=175°−70°=105°

Question 23:

In Fig., write all pairs of adjacent angles and all the linear pairs.

Answer 23:

Adjacent angles:

∠DOA and ∠DOC
∠DOC and ∠BOC

∠AOD and ∠DOB
∠BOC and ∠AOC

Linear pairs of angles:

∠AOD and ∠DOB
∠BOC and ∠AOC

Question 24:

In Fig. 25, find ∠x. Further find ∠BOC, ∠COD and ∠AOD.

Answer 24:

∠AOD+∠DOC+∠COB=180°(Linear pair)

(x+10)°+x°+(x+20)°=180°
3x+30°=180°
3x=180°−30°
3x=150°

x=150°/3=50°

∠BOC=x+20°=50°+20°=70°
∠COD=x=50°
∠AOD=x+10°=50°+10°=60°

Question 25:

How many pairs of adjacent angles are formed when two lines intersect in a point?

Answer 25:

If two lines intersect at a point, then four adjacent pairs are formed, and those pairs are linear as well.

Question 26:

How many pairs of adjacent angles, in all, can you name in Fig.?

Answer 26:

There are 10 adjacent pairs in the given figure; they are:
∠EOD and ∠DOC
∠COD and ∠BOC
∠COB and ∠BOA

∠AOB and ∠BOD
∠BOC and ∠COE
∠COD and ∠COA
∠DOE and ∠DOB

∠EOD and ∠DOA
∠EOC and ∠AOC
∠AOB and ∠BOE
 

Question 27:

In Fig., determine the value of x.

Answer 27:

∠AOB+∠BOC=180°           (Linear pair)
⇒3x+3x=180°

⇒6x=180°

Question 28:

In Fig., AOC is a line, find x.

Answer 28:

∠AOB+∠BOC=180°                (Linear pair)
⇒70°+2x=180°
⇒2x=180°−70°=110°

Question 29:

In Fig., POS is a line, find x.

Answer 29:

∠QOP+∠QOR+∠ROS=180°       (Angles on a straight line)

⇒60°+4x+40°=180°
⇒100°+4x=180°
⇒4x=180°−100°=80°

Question 30:

In Fig., lines l₁ and l₂ intersect at O, forming angles as shown in the figure. If x = 45°, find the values of y, zand u.

Answer 30:

∠z=∠x=45°       (Vertically opposite angles)
Now,∠x+∠y=180°      (Linear pair)
⇒∠y=180°−45°=135°
∠u=∠y=135°       (Vertically opposite angles)

Question 31:

In Fig., three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.

Answer 31:

∠BOD + ∠DOF + ∠FOA = 180°        (Linear pair)
∴ ∠FOA = ∠u = 180°−90°−50°=40
∠FOA=∠x=40°    (Vertically opposite angles)
∠BOD=∠z=90°    (Vertically opposite angles)
∠EOC=∠y=50°    (Vertically opposite angles)

Question 32:

In Fig., find the values of x, y and z.

Answer 32:

∠y=25°       (Vertically opposite angles)
Since ∠x+∠y=180°         (Linear pair)
∴∠x=180°−25°=155°
∠z=∠x=155°        (Vertically opposite angles)