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MATHS 2 Marks Questions

Parallelograms · UP Board (UPMSP) STD 8 (UPMSP - English Medium). 3 questions.

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Question 12 Marks
The sides of a rectangle are in the ratio $5 : 4$ and its perimeter is $90\ cm$. Find its length and breadth.
Answer
Let the length and breadth of the rectangle be $5x$ and $4x$ respectively.
$\therefore 2(5x + 4x) = 90$
$\Rightarrow 18x = 90$
$\Rightarrow x = 5$
Length of the rectangle is $(5 \times 5) = 25cm$ and breadth $= (4 \times 5) = 20cm.$
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Question 22 Marks
Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?
Answer
Let the measure of each equal angle be $x^\circ .$
$\therefore\text{x}+\text{x}=180^\circ$
$\Rightarrow2\text{x}=180$
$\Rightarrow\text{x}=90$
​​​​​​​Hence, the measure of each angle is $90^\circ .$
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Question 32 Marks
In the given figure $ABCD$ is a square. Find the measure of $\angle\text{CAD}.$
Answer
In $\triangle\text{ADC},$
$\text{DA}=\text{DC}$
$\Rightarrow\angle\text{ACD}=\angle\text{DAC}=\text{x}^\circ$
Then, $\text{x}^\circ+\text{x}^\circ+90^\circ=180^\circ$
$\Rightarrow2\text{x}^\circ=180^\circ-90^\circ$
$\Rightarrow2\text{x}^\circ=90^\circ$
$\Rightarrow\text{x}^\circ=45^\circ$
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