2 Marks Questions

Question 12 Marks

ABCD is a square. AC and BD intersect at O. state the measure of $\angle\text{AOB}$.

Answer

Since, diagonals of a square bisect each other at right angle. Therefore, $\angle\text{AOB}=90^\circ$

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Question 22 Marks

In a parallelogram ABCD, if $\angle\text{D} = 115^\circ,$ then write the measure of $\angle\text{A.}$

Answer

In Parallelogram ABCD, $\angle\text{A}$ and $\angle\text{D}$ are Adjacent angles.
We know that in a parallelogram, adjacent angles are supplementary.
Now, $\angle\text{A}+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{A}+115^\circ=180^\circ$
$\Rightarrow\angle\text{A}=180^\circ-115^\circ$
$\Rightarrow\angle\text{A}=65^\circ$
So, measure of $\angle\text{A}$ is 65°.

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Question 32 Marks

ABCD is a rectangle with $\angle\text{ABD}=40^\circ$. Determine $\angle\text{DBC}$.

Answer

$\angle\text{ABC}=90^\circ$
$\Rightarrow\angle\text{ABD}+\angle\text{DBC}=90^\circ$
$\Rightarrow40^\circ+\angle\text{DBC}=90^\circ$
$\Rightarrow\angle\text{DBC}=50^\circ$

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Question 42 Marks

In a parallelogram ABCD, write the sum of angles A and B.

Answer

In Parallelogram ABCD, $\angle\text{A}$ and $\angle\text{B}$ are adjacent angles.
Thus, AB || DC.
Then, we have $\angle\text{A}$ and $\angle\text{B}$ as consecutive interior angles which must be supplementary.
$\angle\text{A}+\angle\text{B}=180^\circ$
Hence, the sum of $\angle\text{A}$ and $\angle\text{B}$ is 180°.

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Question 52 Marks

The sides AB and CD of a parallelogram ABCD are bisected at E and F. prove that EBFD is a parellelogram.

Answer

Since is a parallelogram. therefore,
AB || DC and AB = DC
⇒ EB || DF and $\frac{1}{2}\text{AB}=\frac{1}{2}\text{DC}$
⇒ EB || DF and EB = DF
⇒ EBFB is a parallelogram.

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Question 62 Marks

In a parallelogram ABCD, determine the sum of angles $\angle\text{C}$ and $\angle\text{D}$.

Answer

$\angle\text{C}$ and $\angle\text{D}$ are cosecutive interior angles on the same side of the transversal CD. Therefore,
$\angle\text{C}+\angle\text{D}=180^\circ$

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Question 72 Marks

In a parallelogram ABCD, if $\angle\text{B}=135^\circ,$ determine the measure of its other angles.

Answer

We have, $\angle \text{B}=135^\circ$
Since ABCD is a parallelogram
$\therefore\angle\text{A}=\angle\text{C},\angle\text{B}=\angle\text{D}$ and $\angle\text{A}+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{A}+135^\circ=180^\circ$
$\Rightarrow\angle\text{A}=45^\circ$
$\Rightarrow\angle\text{A}=\angle\text{C}=45^\circ$ and $\angle\text{B}=\angle\text{D}=135^\circ$

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Question 82 Marks

PQRS is a square such that PR and SQ intersect at O. State the measure of $\angle\text{POQ.}$

Answer

PQRS is a square given as:

Since the diagonals of a square intersect at right angle.
Therefore, the measure of $\angle\text{POQ}$ is 90°.

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