Question

Construct the following quadrilateral: Quadrilateral $\text{TRUE. TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75°, ∠U = 120°}$

Answer 1

Let's draw a rough sketch of the quadrilateral to get an idea about the figure -

In quadrilateral$\text{TRUE}$,

$$\begin{gathered} \text{TR = 3.5 cm} \\ \text{RU = 3 cm} \\ \text{UE = 4 cm} \\ \text{∠R = 75°} \\ \text{∠U = 120°} \end{gathered}$$

Let's construct quadrilateral$\text{TRUE}$ using the above information -

Step 1: Draw a line segment$\text{UE = 3 cm}$, then draw rays $\text{RX and UY}$forming an angle of $\text{75° and 120°}$with line segment $\text{RU}$-

Step 2: Take an arc of radius $\text{3.5 cm}$and cut an arc on ray$\text{RX}$at point $\text{T}$, then change the radius to $\text{4 cm}$and cut an arc on ray $\text{UY}$at point $\text{E}$-

Step 3: Join$\text{TE}$to get the required quardilaetral -

Hence, $\text{TRUE}$ is the required quadrilateral.