Theory:

  • Draw one side and make the angle with their side measure.
       1.PNG
  • Make the existing side \(BC\) another indicated angle.
        2.PNG
  • Mark the new \(Y\) axis point of the new side equal to the length of the specified side.  Mark it as \(D\). 
      3.PNG
  • Join the \(AD\) points in the quadrilateral on the \(4\)th side. The quadrilateral is now complete.
      4.PNG
Example:
Construct a quadrilateral \(TRUE\) with the following measurements.
 
\(TR =\) \(3.5 cm\), \(RU = 3 cm\), \(UE = 4 cm\), \(∠R = 75°\), \(∠U = 120°\).
 
Step 1:  Draw side \(RU = 3 cm\) and angle \(120 ° \) at point \(U\). As the vertex \(E\) is \(4 cm\) away from \(U\), cut the line segment \(UE\) of \(4 cm\) out from this ray.
5.PNG
 
Step 2: Draw the angle \(75 ° \) at the point \(R\). As the vertex \(T\) is \(3.5 cm\) away from the vertex \(R\), cut the line segment \(RT\) away from the \(3.5 cm\) of this ray.
 
6.PNG
 
Step 3: Join \(T\) to \(E\).
 
7.PNG
 
Thus, the \(TRUE\) is the required quadrilateral.