2 Marks Questions

Question 12 Marks

For what value of $x$ will the lines $l$ and $m$ be parallel to each other?

Answer

Lines l and m will be parallel if $3x - 20 = 2x + 10$ [Since, if corresponding angles are equal, lines are parallel]
$\Rightarrow 3x - 2x = 10 + 20$
$ \Rightarrow x = 30$

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Question 22 Marks

Define the following terms: Reflex angle.

Answer

An angle greater than $180^\circ $but less than $360^\circ $is called a reflex angle.

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Question 32 Marks

In the figure given below, state which lines are parallel and why?

Answer

In the given figure, $\angle\text{BAC}=\angle\text{ACD}=110^\circ$ But, these are alternate angles when transversal $AC$ cuts $AB$ and $CD$. Hence, $AB \| CD.$

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Question 42 Marks

Find the angle which is four times its complement.

Answer

Let the measure of the required angle be $x$.
Then, measure of its complement $= (90^\circ - x).$
Therefore, $x = (90^\circ - x)4$
$\Rightarrow x = 360^\circ - 4x$
$\Rightarrow 5x = 360^\circ $
$\Rightarrow x = 72^\circ $
Hence, the measure of the required angle is $72^\circ $.

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Question 52 Marks

Define the following terms: Supplementary angles.

Answer

Two angles are said to be supplementary if the sum of their measures is $180^\circ .$

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Question 62 Marks

Find theangle which is five times its supplement.

Answer

Let the measure of the required angle be $x$ .
Then, measure of its supplement $=\left(180^{\circ}- x \right)$.
Therefore, $x =\left(180^{\circ}- x \right) 5$
$\Rightarrow x=900^{\circ}-5 x $
$ \Rightarrow 6 x=900^{\circ} x=150^{\circ}$
Hence, the measure of the required angle is $150^{\circ}$.

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Question 72 Marks

For what value of $x$ will the lines $l$ and $m$ be parallel to each other?

Answer

$⇔ 3x + 5 + 4x = 180$ [Consecutive Interior Angle] $⇔ 7x = 175 ⇔ x = 25$

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Question 82 Marks

Define the following terms: Obtuse angle.

Answer

An angle greater than $90^\circ $ but less than $180^\circ $ is called an obtuse angle.

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Question 92 Marks

Two lines $AB$ and $CD$ intersect at $O$. If $\angle\text{AOC}=50^\circ,$ find $\angle\text{AOD},\angle\text{BOD}$ and $\angle\text{BOC}.$

Answer

We know that if two lines intersect then the vertically-opposite angle are equal.
Therefore, $\angle\text{AOC}=\angle\text{BOD}=50^\circ$
Let $\angle\text{AOD}=\angle\text{BOC}=\text{x}^\circ$
Also, we know that the sum of all angles around a point is $360^\circ $.
Therefore, $\angle\text{AOC}+\angle\text{AOD}+\angle\text{BOD}+\angle\text{BOC}=360^\circ$
$\Rightarrow 50 + x + 50 + x = 360^\circ$
$\Rightarrow 2x = 260^\circ$
$\Rightarrow x = 130^\circ$
Hence, $\angle\text{AOD}=\angle\text{BOC}=130^\circ$
Therefore, $\angle\text{AOD}=130^\circ,\angle\text{BOD}=50^\circ$ and $\angle\text{BOC}=130^\circ.$

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Question 102 Marks

Find the measure of an angle which is: Equal to its supplement.

Answer

Let the measure of the rquired angle be $x^\circ $.
Then, in case of supplementary angle: $x + x = 180^\circ $
$\Rightarrow 2x = 180^\circ $
$\Rightarrow x = 90^\circ $
Hence, measure of the angle that is equal to its supplement is $90^\circ .$

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Question 112 Marks

Two adjacent angles on a straight line are in the ratio $5 : 4$. Find the measure of each of these angles.

Answer

Let the two adjacent angles be $5x$ and $4x$, respectively.
Then, $5x + 4x = 180^\circ $
$\Rightarrow 9x = 180^\circ $
$\Rightarrow x = 20^\circ $
Hence, the two angles are $5 \times 20^\circ = 100^\circ $ and $4 \times 20^\circ = 80^\circ .$

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Question 122 Marks

Define the following terms: Interior of an angle.

Answer

The interior of an angle is the set of all points in its plane, which lie on the same side of $OA$ as $B$ and also on the same side of as $A.$

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Question 132 Marks

Find the measure of an angle which is: Equal to its complement.

Answer

Let the measure of the required angle be $x^{\circ}$.
Then, in case of complementary angle: $x+x=90^{\circ} $
$\Rightarrow 2 x=90^{\circ} $
$\Rightarrow x=45^{\circ}$
Hence, measure of the angle that is equal to its complement is $45^{\circ}$.

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Question 142 Marks

Define the following terms: Angle.

Answer

rays $OA$ and $OB$, with a common end-point $O$, form an angle $AOB$ that is represented as $\angle\text{AOB}.$

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Question 152 Marks

In the adjoining figure, what value of x will make $AOB$ a straight line?

Answer

AOB will be a straight line if $3 x+20+4 x-36=180^{\circ} $
$\Rightarrow 7 x=196^{\circ} $
$\Rightarrow x=28^{\circ}$
Hence, $x=28$ will make AOB a striaght line.

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Question 162 Marks

Two complementary angles are in the ratio $4 : 5$. Find the angles.

Answer

Let the angles be $4 x$ and $5 x$, respectively.
Then, $4 x+5 x=90 $
$\Rightarrow 9 x=90 $
$\Rightarrow x=10^{\circ}$
Hence, the two angles are $4 x=4 \times$
$10^{\circ}=40^{\circ}$ and $5 x=5 \times 10^{\circ}=50^{\circ}$.

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Question 172 Marks

Define the following terms: Complementary angles.

Answer

Two angles are said to be complementry if the sum of their measures is$ 90^\circ .$

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Question 182 Marks

Find the measure of an angle which is $36^\circ $ more than its complement.

Answer

Let the measure of the required angle be $x^\circ .$
then, measure of its complement $= (90 - x)^\circ .$
Therefore, $x - (90^\circ - x) = 36^\circ $
$\Rightarrow 2x = 126^\circ $
$\Rightarrow x = 63^\circ $
Hence, the measure of the required angle is $63^\circ .$

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Question 192 Marks

In the adjoining figure, $AOB$ is a straight line. Find the value of $x.$

Answer

We know that the sum of angles in a linear pair is $180^\circ .$
Therefore, $\angle\text{AOC}+\angle\text{BOC}=180^\circ$
$\Rightarrow 62^\circ + x^\circ = 180^\circ $
$\Rightarrow x^\circ = (180^\circ - 62^\circ ) $
$\Rightarrow x = 118^\circ $
Hence, the value of $x$ is $118^\circ .$

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