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Maths 2 Marks Questions

Lines and Angles · Jharkhand Board (JAC) STD 7 (Jharkhand - English Medium). 46 questions.

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Question 12 Marks
Find the value of $x$ in the following figure.
Answer
Since, $\angle \text{BOA}+\angle \text{BOC}=180^\circ$ Linear pair:
$\Rightarrow 60^\circ + x^\circ = 180^\circ$
$ \Rightarrow x^\circ = 180^\circ - 60^\circ $
$\Rightarrow x^\circ = 120^\circ$
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Question 22 Marks
In Figure, state which lines are parallel and why?
Answer
Let, $F$ be the point of intersection of the line $CD$ and the line passing through point $E$.
Here, $\angle \text{ACD}$ and $\angle \text{CDE}$ are alternate and equal angles.
So, $\angle \text{ACD}=\angle \text{CDE}=100^\circ$
Therefore, $\text{AC}||\text{EF}$
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Question 32 Marks
Find the value of $x$ in the following figure.
Answer
Linear pair: $\Rightarrow 3\text{x}^\circ+2\text{x}^\circ=180^\circ$
$\Rightarrow 5\text{x}^\circ=180^\circ$
$\Rightarrow \text{x}^\circ-\frac{180^\circ}{5}$
$\Rightarrow \text{x}^\circ=36^\circ$
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Question 42 Marks
Find the value of $x$ in the following figure.
Answer
Linear pair:
Since, $35^\circ + x^\circ + 60^\circ = 180^\circ $
$\Rightarrow x^\circ = 180^\circ – 35^\circ - 60^\circ $
$\Rightarrow x^\circ = 180^\circ - 95^\circ $
$\Rightarrow x^\circ = 85^\circ $
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Question 52 Marks
In Figure, lines $l_1$ and $l_2$ intersect at $O$, forming angles as shown in the figure. If $x = 45^\circ $, find the values of $y, z$ and $u$.
Answer
$\angle \mathrm{z}=\angle \mathrm{x}=45^{\circ}$ (Vertically opposite angles)
Now,
$\angle \mathrm{x}+\angle \mathrm{y}=180^{\circ} \text { (Linear pair) }$
$\Rightarrow \angle \mathrm{y}=180^{\circ}-45^{\circ}=135^{\circ}$
$\angle \mathrm{u}=\angle \mathrm{y}=135^{\circ}$ (Vertically opposite angles
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Question 62 Marks
In fig. write down. Each pair of vertically opposite angles.
Answer
The two angles formed by two intersecting lines and have no common arms are called vertically opposite angles.
$\angle1 \text{ and }\angle4$
$\angle2 \text{ and }\angle3$
$\angle5 \text{ and }\angle8$
$\angle6 \text{ and }\angle7$
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Question 72 Marks
Can two obtuse angles be supplementary, if both of them be. Obtuse?
Answer
No, two obtuse angles cannot be supplementary. Because, the sum of two angles is greater than $90^\circ $ so their sum will be greater than $180^\circ $.
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Question 82 Marks
If the supplement of an angle is $65^\circ $, then find its complement.
Answer
Let $x$ be the required angle
So,
$\Rightarrow x + 65^\circ = 180^\circ $
$\Rightarrow x = 180^\circ - 65^\circ $
$= 115^\circ $
But the complement of the angle cannot be determined.
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Question 92 Marks
Find the value of $x$ in the following figure.
Answer
Linear pair:
$3\text{x}^\circ=105^\circ$
$\Rightarrow\text{x}^\circ=\frac{105^\circ}{3}$
$\Rightarrow\text{x}^\circ=45^\circ$
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Question 102 Marks
Find the value of $x$ in the following figure.
Answer
Linear pair: $83^\circ + 92^\circ + 47^\circ + 75^\circ + x^\circ = 360^\circ$
$ \Rightarrow x^\circ + 297^\circ = 360^\circ$
$ \Rightarrow x^\circ = 360^\circ – 297^\circ $
$\Rightarrow x^\circ = 63^\circ$
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Question 112 Marks
Find the value of $x$ in the following figure.
Answer
Linear pair: $3\text{x}^\circ+2\text{x}^\circ+\text{x}^\circ+2\text{x}^\circ=360^\circ$
$\Rightarrow8\text{x}^\circ=360^\circ$
$\Rightarrow \text{x}^\circ=\frac{360^\circ}{8}$
$\Rightarrow \text{x}^\circ=45^\circ$
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Question 122 Marks
In Figure, $AB\ ||\ CD$ and $AC\ ||\ BD$. Find the values of $x, y, z$.
Answer
Here, $AC\ ||\ BD$ and $CD\ ||\ AB$ Alternate interior angles,
$\angle \text{DCA}=\text{x}=40^\circ$
$\angle \text{DAB}=\text{y}=35^\circ$
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Question 132 Marks
Name the four pairs of supplementary angles shown in Figure.
Answer
The supplementary angles are:
$\angle \text{AOC}\text{ and }\angle\text{COB}$
$\angle \text{BOC}\text{ and }\angle\text{DOB}$
$\angle \text{BOD}\text{ and }\angle\text{DOA}$
$\angle \text{AOC}\text{ and }\angle\text{DOA}$
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Question 142 Marks
In Figure, $AOC$ is a line, find $x$.
Answer
$\angle \text{AOB}+\angle \text{BOC}=180^\circ$ Linear pair,
$\Rightarrow 2\text{x}+70^\circ=180^\circ$
$\Rightarrow 2\text{x}=180^\circ-70^\circ$
$\Rightarrow 2\text{x}=110^\circ$
$\Rightarrow \text{x}=\frac{110^\circ}{2}$
$\Rightarrow \text{x}=55^\circ$
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Question 152 Marks
Can two obtuse angles be supplementary, if both of them be.
Right?
Answer
Yes, two right angles can be supplementary.
Because, $90^\circ + 90^\circ = 180^\circ $
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Question 162 Marks
In Figure, determine the value of $x$.
Answer
Linear pair: $\angle \text{COB}+\angle \text{AOB}=180^\circ$
$\Rightarrow 3\text{x}^\circ+3\text{x}^\circ=180^\circ$
$\Rightarrow 6\text{x}^\circ=180^\circ$
$\Rightarrow \text{x}^\circ=\frac{180^\circ}{6}$
$\Rightarrow \text{x}^\circ=30^\circ$
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Question 172 Marks
In fig. the corresponding arms of $\angle \text{ABC}$ and $\angle \text{DEF}$ are parallel. $\angle \text{ABC}=75^\circ,$ find $\angle \text{DEF}.$
Answer

Construction: Let $G$ be the point of intersection of lines $BC$ and $DE$.
​​​​​​​$\because \text{AB}||\text{DE}$ and $\text{BC}||\text{EF}$
$\therefore \text{ABC}=\angle \text{DGC}=\angle \text{DEF}=75^\circ$ (Corresponding angles)
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Question 182 Marks
In Figure, $POS$ is a line, find $x$.
Answer
Angles of a straight line, $\angle \text{QOP}+\angle \text{QOR}+\angle \text{ROS}=108^\circ$
$\Rightarrow 60^\circ+4\text{x}+40^\circ=180^\circ$
$\Rightarrow 100^\circ+4\text{x}=180^\circ$
$\Rightarrow 4\text{x}=180^\circ-100^\circ$
$\Rightarrow4\text{x}=80^\circ$
$\Rightarrow \text{x}=\frac{80^\circ}{4}$
$\Rightarrow\text{x}=20^\circ$
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Question 192 Marks
Can two obtuse angles be supplementary, if both of them be.
Acute?
Answer
No, two acute angle cannot be supplementary.
Because, the sum of two angles is less than 90º so their sum will also be less tha 90º.
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Question 202 Marks
In Figure, 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
$\angle \text{BOD}+\angle \text{DOF}+\angle \text{FOA}=180^\circ$ (Linear pair)
$\therefore \angle \text{FOA}=\angle \text{u}=180^\circ-90^\circ-50^\circ=40^\circ$
$\angle \text{FOA}=\angle \text{x}=40^\circ$ (Vertically opposite angles)
$\angle \text{BOD}=\angle \text{z}=90^\circ$ (Vertically opposite angles)
$\angle \text{EOC}=\angle \text{y}=50^\circ$ (Vertically opposite angles)
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Question 212 Marks
In Figure, find the values of $x, y$ and $z$.
Answer
$\angle \text{y}=25^\circ$ (Vertically opposite angles)
Since, $\angle \text{x}+\angle \text{y}=180^\circ$ (Linear pair)
$\therefore \angle \text{x}=180^\circ-25^\circ=155^\circ$
$\angle \text{z}=\angle \text{x}=155^\circ$ (Vetically opposite angles)
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Question 222 Marks
In fig. write down. Each linear pair.
Answer
The two adjacent angles are said to form a linear pair of angles if their non-common arms are two opposite rays. $\angle1 \text{ and }\angle3$
$\angle1 \text{ and }\angle2$
$\angle4 \text{ and }\angle3$
$\angle4 \text{ and }\angle2$
$\angle5 \text{ and }\angle6$
$\angle5 \text{ and }\angle7$
$\angle6 \text{ and }\angle8$
$\angle7 \text{ and }\angle8$
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Question 322 Marks
In Fig.(ii) name all the pairs of adjacent angles.
Image
Answer
$\angle A D B, \angle A D C ; \angle B A D, \angle D A C$
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Question 332 Marks
In Fig. 12.18, A, B, C are collinear points and $\angle D B A=\angle E B A$.
Name two pairs of supplementary angles.
Image
Answer
$\angle A B E, \angle E B C ; \angle A B D, \angle D B C$
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Question 362 Marks
In Fig.(ii) write down: (ii) each pair of vertically opposite angles.
Image
Answer
$\angle 1, \angle 4 ; \angle 2, \angle 3 ; \angle 5, \angle 8 ; \angle 6, \angle 7$
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Question 382 Marks
In Fig.(i) name all the pairs of adjacent angles.
Image
Answer
$\angle D A C, \angle C A B ; \angle A C B, \angle F C B ; \angle A B C, \angle A B E$
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Question 392 Marks
In Fig. $A, B, C$ are collinear points and $\angle D B A=\angle E B A$.
Name two linear pairs
Image
Answer
$\angle A B E, \angle E B C ; \angle A B D, \angle D B C$
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Question 452 Marks
Name the four pairs of supplementary angles shown in Fig.
Image
Answer
$\angle A O C, \angle C O B ; \angle C O B, \angle B O D ; \angle B O D, \angle D O A ; \angle D O A, \angle A O C$
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Question 462 Marks
Identify the complementary and supplementary pairs of angles from the following pairs:
(i) $25^{\circ}, 65^{\circ}$
(ii) $120^{\circ}, 60^{\circ}$
(iii) $63^{\circ}, 27^{\circ}$
(iv) $100^{\circ}, 80^{\circ}$
Answer
Complementary :(i), (iii)
Supplementary :(ii), (iv)
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