Question

Construct a quadrilateral with three sides and two angles given.

Answer 1

Step 1: Making assumption

Let us say we are required to construct a quadrilateral $\mathrm{PQRS}$ where the measurements are:

$\mathrm{QR}=6\mathrm{cm}$

$\mathrm{RS}=5\mathrm{cm}$

$\mathrm{PS}=4\mathrm{cm}$

$\angle \mathrm{S}=100°$

$\angle \mathrm{R}=120°$

Step 2: Constructing the quadrilateral

Now starting with the construction, the steps are:

Draw a line segment of length $5\mathrm{cm}$ and mark the ends as $\mathrm{S}$ and $\mathrm{R}$.

Using a protractor, draw a line from point $\mathrm{R}$ making $120°$ and another line from point $\mathrm{S}$ making $100°$ with the line segment $\mathrm{SR}$.

Set your compass to the radius of $4\mathrm{cm}$ and make an arc from the point $\mathrm{S}$ on the $100°$ line. Mark the point as $\mathrm{P}$ where the arc intersects the line.

Similarly, set the compass to the radius of $6\mathrm{cm}$ and make an arc from point $\mathrm{R}$ on the $120°$ line. Mark the point as $\mathrm{Q}$ where the arc intersects the line.

Join the points $\mathrm{P}$ and $\mathrm{Q}$.

Thus, we obtain the quadrilateral $\mathrm{PQRS}$ of the required measurements.