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:
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