Question
Construct a quadrilateral $PQRS$, where $PQ = 3.5\ cm, QR = 6.5\ cm$, $\angle\text{P}=\angle\text{R}=105^\circ$ and $\angle\text{S}=75^\circ$
✓
Answer
We know that the sum of all the angles in a quadrilateral is $360$.
i.e., $\angle\text{P}+\angle\text{Q}+\angle\text{R}+\angle\text{S}+360^\circ$
$\Rightarrow\angle\text{Q}=75^\circ$
Steps of construction:
Step $I$: Draw $PQ = 3.5\ cm$.
Step $II$: Construct $\angle\text{XPQ}=105^\circ$ at $P$ and $\angle\text{PQY}=75^\circ$ at $Q$.
Step $III$: With $Q$ as the centre and radius $6.5\ cm$, cut off $QR = 6.5$
Step $IV$: At $R$, draw $\angle\text{QRZ}=105^\circ$ such that it meets $PX$ at $S$.
The quadrilateral so obtained is the required quadrilateral.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Verify the division algorithm i.e., Dividend = Divisor $\times $ Quotient + Remainder, in the following.
Also write the quotient and remainder.
Dividend: $15\text{y}^4-16\text{y}^3+9\text{y}^2-\frac{10}{3}\text{y}+6$
Divisor: $3\text{y}-2$
→Also write the quotient and remainder.
Dividend: $15\text{y}^4-16\text{y}^3+9\text{y}^2-\frac{10}{3}\text{y}+6$
Divisor: $3\text{y}-2$
A tank open at the top is made of iron sheet $4m$ wide. If the dimensions of the tank are $12m \times 8m \times 6m$, find the cost of iron sheet at $Rs. 17.50$ per metre.
→Amit earns $Rs. 32000$ per month. He spends $\frac{1}{4}$ of his income of food; $\frac{3}{10}$ of the remainder on house rent and $\frac{5}{21}$ of the remainder on the education of children. How much money is still left with him$?$
→A bag contains $4$ red, $5$ black and $6$ white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:
$i.$ white
$ii.$ red
$iii.$ not black
$iv.$ red or white
→$i.$ white
$ii.$ red
$iii.$ not black
$iv.$ red or white
Simplify: $(5 - x)(6 - 5x)( 2 - x)$
→Write down the product of $-8x^2y^6$ and $-20xy$. Verify the product for $x = 2.5, y = 1.$
→Solve the following equation and verify your answer: $\frac{(\text{x}+2)(2\text{x}-3)-2\text{x}^2+6}{\text{x}-5}=2$
→The following table depicts the maximum temperature on the seven days of a particular week. Study the table and draw a line graph for the same.
→|
Day
|
Sun
|
Mon
|
Tues
|
Wed
|
Thurs
|
Fri
|
Sat
|
|
Maximum temp. (in $^\circ C)$
|
$25$
|
$28$
|
$26$
|
$32$
|
$29$
|
$24$
|
$31$
|
Three years ago, the population of a town was $50000$. If the annual increase during three successive years be at the rate of $4\%$, $5\%$ and $3\%$ respectively, find the present population.
→Ahmed buys a plot of land for $Rs. 480000.$ He sells of it at a loss of $6\%.$ At what gain percent should he sell the remaining part of the plot to gain $10\%$ on the whole$?$
→