Question

Construct the following quadrilateral: Quadrilateral$\text{PLAN. PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°}$

Answer 1

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

In quadrilateral$\text{PLAN}$,

$$\begin{gathered} \text{PL = 4 cm} \\ \text{LA = 6.5 cm} \\ \text{∠P = 90°} \\ \text{∠A = 110°} \\ \text{∠N = 85°} \end{gathered}$$

From the figure, we can see that for constructing a quadrilateral$\text{PLAN}$, we need the value of $\angle L.$

By angle sum property of quadrilateral -

$$\begin{gathered} \angle A+\angle N+\angle P+\angle L=360° \\ 110°+85°+90°+\angle P=360° \\ \angle P=360°-285°=75° \end{gathered}$$

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

Step 1: Draw a line segment$\text{PL = 4 cm}$, then draw rays $\text{PX and LY}$forming an angle of $\text{90° and 75°}$with line segment $\text{PL}$-

Step 2: Take an arc of radius $\text{6.5 cm}$and cut an arc from point $\text{L}$ on the ray$\text{LY}$, which intersect at point $\text{A}$ -

Step 3: Draw a ray$\text{AZ}$which is making an angle of$110°$with line segment$\text{LA}$ and intersect ray$\text{PX}$at point$\text{N}$-

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