2 Marks Questions

Question 12 Marks

In the given figure, the arms of two angles are parallel. If $\angle ABC = 70^\circ$, then find $\angle DGC$

Answer

From the figure, it is clear that $AB$ is parallel to $DG$ and there is a transversal line $BC$ that is intersecting them
Therefore, $\angle DGC = \angle ABC$ (Corresponding angles)
Given that:
$\angle ABC = 70^\circ$
Therefore,
$\angle DGC = \angle ABC = 70^\circ$
Hence,
The value of $\angle DGC$ is equal to $70^\circ$

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Question 22 Marks

Find the value of $x$ in the figures if $l \| m$

Answer

From the above figure it can be clearly seen that:
$\angle x$ is equal to $100^\circ$ as they are corresponding angles
Therefore, $\angle x = 100^\circ$

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Question 32 Marks

Find the value of $x$ in the figure below, if $l \| m$

Answer

From the above figure, we have

$\angle y = 110^\circ$ (Corresponding angles)
Also,
$\angle x and \angle y$ form a linear pair of angles. Therefore,
$\angle x + \angle y = 180^\circ$ (Linear pair)
$\angle x + 110^\circ = 180^\circ $
$x = 180^\circ - 110^\circ $
$ \angle x = 70^\circ$
Hence, value of $\angle x$ is $70^\circ$

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Question 42 Marks

In the figure given below:

Are $\angle BOD$ and $\angle DOA$ supplementary?

Answer

Yes, $\angle BOD$ and $\angle DOA$ are supplementary because:
These angles add up to $180^{\circ} .$

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Question 52 Marks

Can two angles be supplementary, if both of them are right?

Answer

Yes. If both the angles are right angles then the pair of angles must be supplementary because:
Right angle is equal to $90^{\circ}$ and addition of two right angles is equal to $180^{\circ}$
i.e., $90^{\circ}+90^{\circ}=180^{\circ}$
Hence, Two right angles form a supplement pair of angles.

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Question 62 Marks

Can two angles be supplementary, if both of them are obtuse?

Answer

Two obtuse angles can’t be supplementary because:
Obtuse angle is always greater than $90^{\circ}$ and addition of any two angles greater than $90^{\circ}$ can never be equal to $180^{\circ}$
Hence, Two obtuse angles cannot be in a supplementary angle pair.

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Question 72 Marks

Can two angles be supplementary, if both of them are acute?

Answer

Two Acute angles can’t be supplementary because:
Acute angle is always less than $90^{\circ}$ and addition of any two angles less than $90^{\circ}$ can never be equal to $180^{\circ}$
Hence, Two acute angles cannot be in a supplementary angle pair

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Question 82 Marks

In the given figure, $\angle 1$ and $\angle 2$ are supplementary angles. If $\angle 1$ is decreased, what changes should take place in $\angle 2$ so that both the angles still remain supplementary?

Answer

Since, $ \angle 1$ and $ \angle 2$ are Supplementary angles
And if $ \angle 1$ is decreased than $ \angle 2$ must be increased by the same measure, so that the pair of both the angles remain supplementary. Here $ \angle 1$ is reduced by $1$ degree, so $ \angle 2$ must be increased by $1$ degree.

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Question 92 Marks

Find the angle which equal to its supplement.

Answer

Let the angle be $x^\circ $
Its supplement $= 180^\circ – x^\circ $
According to the question,
$x^\circ = 180^\circ – x^\circ $
$ \Rightarrow x^\circ + x^\circ = 180^\circ $
$ \Rightarrow 2x^\circ = 180^\circ $
$ \Rightarrow x^\circ = \frac{180^{\circ}}{2} = 90^\circ $
Hence, the required angle is $90^\circ .$

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Question 102 Marks

Find the angle which is equal to its complement.

Answer

Let the angle be $x^\circ $
Its complement $= 90^\circ – x^\circ $
According to the question,
$x^\circ = 90^\circ – x^\circ $
$ \Rightarrow x^\circ + x^\circ = 90^\circ $
$ \Rightarrow 2x^\circ = 90^\circ $
$ \Rightarrow x^\circ = \frac{90^{\circ}}{2} = 45^\circ $

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Question 112 Marks

Identify whether the pair of angles are complementary or supplementary: $80º, 10º$

Answer

We know that two angles are complementary if their sum is $90^{\circ}$
Here, the Sum of the measures of the given pair of angles $=80^{\circ}+10^{\circ}=90^{\circ}$
As the sum of these angles is equal to $90^{\circ}$
Therefore, these angles are complementary angles.

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Question 122 Marks

Identify whether the pair of angles are complementary or supplementary: $45º, 45º$.

Answer

Two angles are complementary, if their sum is $90^{\circ}$
Sum of the measures of given pair of angles $=45^{\circ}+45^{\circ}=90^{\circ}$
As the sum of these angles is equal to $90^{\circ}$
Therefore,
These angles are complementary angles.

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Question 132 Marks

Identify whether the pair of angles are complementary or supplementary: $130º, 50º$.

Answer

Two angles are said to be supplementary if their sum is $180^{\circ}$.
It is given in the question that,
The given pair of angles is $130^{\circ}$ and $50^{\circ}$
and sum of the measures of these angles $=130^{\circ}+50^{\circ}=180^{\circ}$
As the sum of these angles is equal to $180^{\circ}$
Therefore, these angles are supplementary angles.

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Question 142 Marks

Identify the pair of angles are complementary or supplementary: $63º, 27º$.

Answer

We know that:
Two angles are complementary if sum of their measures is $90^{\circ}$
Here, the pair of angles is $63^{\circ}$ and $27^{\circ}$
Sum of the measures of these angles $=63^{\circ}+27^{\circ}=90^{\circ}$
As the sum of these angles is equal to $90^{\circ}$
Therefore, these angles are complementary angles.

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