Question
Construct a quadrilateral $\text{ABCD}$ in which ; $\angle A = 120^\circ , \angle B = 60^\circ , AB = 4 \ cm, BC = 4.5 \ cm$ and $CD = 5 \ cm.$

Answer

The rough figure is as follow :

The Actual figure is constructed as follow

Steps :
  1. Draw $AB = 4 \ cm$.
  2. At $A$, draw $\angle PAB = 120^\circ$ .
  3. At $B$, draw $\angle QBA = 60^\circ$ .
  4. From $BQ$, cut $BC = 4.5 \ cm$.
  5. From $C$, draw an arc of radius $5 \ cm$ which meets $AP$ at $D$.
  6. Join $CD$.
    Thus $\text{ABCD}$ 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.

Start Generating Free

Similar questions

The figure, given below, shows a pentagon $\text{ABCDE}$ with sides $AB$ and $ED$ parallel to each other, and $\angle B : \angle C : \angle D = 5: 6: 7$.
$(i)\  $Using the formula, find the sum of the interior angles of the pentagon. $(ii)$ Write the value of $\angle A + \angle E\ (iii)\ $ Find angles $B, C$ and $D$.
 
A ready$-$made garments shop in Delhi, allows a $20$ percent discount on its garments and still makes a profit of $20$ percent. Find the marked price of a dress which is bought by the shop$-$keeper for $Rs.400.$
In a hexagon $\text{ABCDEF}$, side $AB$ is parallel to side $FE$ and $\angle B : \angle C : \angle D : \angle E = 6 : 4 : 2 : 3$. Find $\angle B$ and $\angle D.$
John lent $Rs. 2550$ to Mohan at $7.5$ percent per annum. If Mohan discharges the debt after $8$ months by giving an old black and white television and $Rs. 1422.50\ ;$ find the price of the television.
Which of the following are cubes of an even number $216, 729, 3375, 8000, 125, 343, 4096$ and $9261.$
The length, breadth, and height of a cuboid $($rectangular solid$)$ are $4 : 3: 2. \ (i)$ If its surface area is $2548\  cm^2$, find its volume.$(ii)$ If its volume is $3000\  m^3$, find its surface area.
$A$ can do a piece of work in $24$ days, $A$ and $B$ can do it in $16$ days and $A, B,$ and $C$ in $10 \frac{2}{3}$ days. In how many days can $A$ and $C$ do it working together?
If $A = \{x ∈ W : 5 < x < 10\}, B = \{3, 4, 5, 6, 7\}$ and $C = \{x = 2n; n ∈ N$ and $n ≤4\}$. Find : $(B ∪ A) ∩ (B ∪ C)$
Gautam takes a loan of $₹ .16,000$ for $2$ years at $15\%$ p.a. compound interest. He repays $₹. 9,000$ at the end of the first year. How much must he pay at the end of the second year to clear the debt?
A can finish a piece of work in $15$ days and $B$ can do it in $10$ days. They worked together for $2$ days and then $B$ goes away. In how many days will $A$ finish the remaining work?