Question

Construct the following quadrilateral: Quadrilateral $\text{MORE}$, $\text{MO = 6 cm, OR = 4.5 cm, ∠M = 60°, ∠O = 105°, ∠R = 105°}$

Answer 1

Let's draw a rough sketch of the quadrilateral $\text{MORE}$, to get the idea of it -

$$\begin{gathered} \text{MO = 6 cm,} \\ \text{OR = 4.5 cm,} \\ \text{∠M = 60°,} \\ \text{∠O = 105°,} \\ \text{∠R = 105°} \end{gathered}$$

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

Step 1: Draw a line segment$\text{MO = 6 cm}$, using the ruler -

Step 2: Construct rays$\text{MX and OY}$, which are making $\text{60° and 105°}$ with the line segment MO -

Step 3: Take an arc of radius$\text{4.5 cm}$, cut an arc on ray$\text{OY}$, which intersects at $\text{R}$ and then constructs ray $\text{RZ}$ which forms $\angle 105°$with $\text{RO}$ -

Point of intersection of ray $\text{RZ}$ and $\text{MX}$ is $\text{E}$ and $\text{MORE}$ is required quadrilateral.

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