SChand Composite Mathematics Class 7 Chapter 10 Lines and Angles Exercise 10B

Exercise 10B 

Question 1

Find each one of the  angles giving reasons : 

Type 1: On alternate Angles: 

1 (i) (IMAGE TO BE ADDED)

Ans: $\angle a=70^{\circ}$

Interior alt. angle 

(ii)  (IMAGE TO BE ADDED)

Ans: $\angle a=105^{\circ}$

(iii) (IMAGE TO BE ADDED)

Ans: $\angle a=70^{\circ}$

$\angle b=40^{\circ}$

(iv)   (IMAGE TO BE ADDED)

Ans: $\angle x=25^{\circ} ; y=35^{\circ}$

Question 2

Type 2: On corresponding angles:

(i)   (IMAGE TO BE ADDED)

(ii)  (IMAGE TO BE ADDED)

$\angle x=130^{\circ}$

(iii) (IMAGE TO BE ADDED)

$\angle a=60^{\circ}$

(iv) (IMAGE TO BE ADDED)

Ans: $\angle x=60^{\circ}$

$\angle y=50^{\circ}$

Question 3

Type 3: 

(i)  (IMAGE TO BE ADDED)

Ans: $\angle a=120^{\circ}$

(ii) (IMAGE TO BE ADDED)  

Ans: $100+\angle a=180^{\circ}$

$\angle a=180-100=80^{\circ}$

(iii) (IMAGE TO BE ADDED)  

Ans: $2 a+3 a=180^{\circ}$

$5 a=180^{\circ}$

$a=\frac{180}{5}=36^{\circ}$

(iv)(IMAGE TO BE ADDED)  

Ans: $110^{\circ}+b=180^{\circ}$

$b=70^{\circ}$

$60+a=180^{\circ}$

$\angle a=120^{\circ}$

Question 4

(IMAGE TO BE ADDED)

Sol: $\angle b=50^{\circ}$ [corresponding angle]

$\angle a=\angle b=50^{\circ}$ [vertical angle]

$\angle d=\angle b=50^{\circ}$ [corr. angle ]

=$\angle C+\angle d=180^{\circ}$[By c.p]

$\Rightarrow \angle C+50^{\circ}=180^{\circ}$

$\Rightarrow \angle C=180^{\circ}-50^{\circ} \Rightarrow \angle C=130^{\circ}$

Question 5

(IMAGE TO BE ADDED)

Sol: $\angle a=\angle 1+\angle 2$

$\angle 1=25^{\circ}$ [Alt .angle]

$\angle 2=65^{\circ} \quad[a l t$ angle $]$

$\angle a=25^{\circ}+65^{\circ}=90^{\circ}$

$\angle a=90^{\circ} \mathrm{Ans}$

Question 6

(IMAGE TO BE ADDED)

Sol: $\Rightarrow \quad x+3 x=120^{\circ}$

$\Rightarrow \quad x=\frac{120^{\circ}}{5}$

$\Rightarrow x=24^{\circ}$ answer 

Question 7

State whether each pair of dotted lines in the following diagram are parallel or not parallel. Give reasons .

(i) (IMAGE TO BE ADDED)

Sol: $105+75^{\circ}$

= 180 yes 

(ii) (IMAGE TO BE ADDED) 

Sol:  ( by alternate angle )

yes

(iii) (IMAGE TO BE ADDED) '

Sol: 130+55キ 180

No

(iv) (IMAGE TO BE ADDED) 

Sol: 91+99キ 180

No

(v)  (IMAGE TO BE ADDED) 

Sol: yes 

(vi)  (IMAGE TO BE ADDED) 

Sol: yes 

(vii)  (IMAGE TO BE ADDED) 

Sol: 

Question 8

Refer to the figure. In each case state that rule or rules justifying the statement. 

 (IMAGE TO BE ADDED) 

(i) If $\angle a=85^{\circ}$ and $\angle b=85^{\circ}$, then $A B \| C D$. -Corresponding angle

(ii) If $\angle b=89^{\circ}$ and $\angle c=89^{\circ}$, then $E F \| G H$. - Alternate angle 

(iii) If $\angle a=110^{\circ}$ and $\angle b=110^{\circ}$, then $A B \| C D$.- Corresponding angle

(iv) If $\angle b=90^{\circ}$ and $\angle c=90^{\circ}$, then $E F \| G H$.- Alternate angle 

Question 9

Find x in the following figures: 

(i)   (IMAGE TO BE ADDED) 

$(A B \| C D)$

Sol: x +3x= 180

4x= 180

x = $\frac{180}{4}$

$x = 45^{\circ}$

(ii)   (IMAGE TO BE ADDED) 

$(P O \| R S)$

Sol: 3x = 90 

x= 30 

3x = $3\times 30= 90^{\circ}$

(iii)   (IMAGE TO BE ADDED) 

$(P Q \| R S)$'

Sol: 3x+ 30 = 180 

3x= 150

x= $\frac{150}{3}$

x = 50 

Question 10

In the figure given below DE||AB, and find the values of a and b 

  (IMAGE TO BE ADDED) 

Sol: 

Question 11

In the figure, $\angle 1=65^{\circ}, \angle 2=65^{\circ}$ and is $p \| q$. Give reasons.

  (IMAGE TO BE ADDED) 

Sol: 

Question 12

In the given figure, $p \| q$ and $r \| s$. Find the angles $a, b$ and $c$.

  (IMAGE TO BE ADDED) 

Sol: $\angle a =80^{\circ}$(vertically opposite angle)

=$\angle c + \angle a$= 180(by linear pair)

= $\angle c$= 180-80= 100

$\angle b$= 100(corresponding angle )

Question 13

In the figure $B D \| C E$, find $x, y$.

  (IMAGE TO BE ADDED) 

Sol: x= 70(by alternate angle )

120 +y= 180 

y= 60

Question 14

In the given figure, $A B\|C D\| F E$, find the angles $x$ and $y$.

  (IMAGE TO BE ADDED) 

Sol: