Theory:

Let us learn how to construct a triangle if the measures of \(2\) of its angles and the length of the side included between them are known. To construct a triangle, first we shall draw a rough diagram which gives an idea where the sides would be. Let us consider an example.
Example:
Construct a triangle \(ABC\) whose measurements are \(AB = 8 \ cm\), \(\angle CAB = 60^{\circ}\) and \(\angle ABC = \angle 40^{\circ}\).
 
Solution:
 
Step 1: First, we shall draw the rough figure of the triangle \(ABC\) with the given measurements.
 
17.png
 
Step 2: Draw a line segment \(AB\) of length \(8 \ cm\).
 
18.png
 
Step 3: Place the protractor at \(A\), draw \(\angle XAB\) making an angle of \(\angle 60^{\circ}\).
 
19.png
 
Step 4: Place the protractor at \(B\), draw \(\angle YBA\) making an angle of \(40^{\circ}\).
 
20.png
 
Step 5: The point \(C\) lies at the intersection of two rays \(AX\) and \(BY\).
 
21.png
 
Therefore, \(ABC\) is the required triangle.