Question

Construct the following quadrilateral.
Quadrilateral $PLAN$ where
$PL=4cm$
$LA=6.5cm$
$\angle P={90}^{\circ }$
$\angle A={110}^{\circ }$
$\angle N={85}^{\circ }$

Answer 1

We know that the sum of all angles of a quadrilateral is ${360}^{\circ }$

$\angle P+\angle L+\angle A+\angle N={360}^{\circ }$

$\Rightarrow$ ${90}^{\circ }+\angle L+{110}^{\circ }+{85}^{\circ }={360}^{\circ }$

$\Rightarrow$ ${285}^{\circ }+\angle L={360}^{\circ }$

$\therefore$ $\angle L={75}^{\circ }$

$\left(1\right)$ Draw line segment $PL=4cm$

$\left(2\right)$ Now, take $P$ as center and draw angle of ${90}^{\circ }$ with the help of protractor.

$\left(3\right)$ Draw ${75}^{\circ }$ angle at point $L$ with the help of protractor.

$\left(4\right)$ Cut off $LA=6.5cm$ with help of a compass with centre $L$ and radius $6.5cm$.

$\left(5\right)$ Now, with the help of a protractor, draw ${110}^{\circ }$ from point $A$.

$\left(6\right)$ Mark point $N$ where the lines from point $P$ and point $A$ intersect .

$\therefore$ $PLAN$ is required quadrilateral.