### 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.

Step 2: Draw a line segment $$AB$$ of length $$8 \ cm$$.

Step 3: Place the protractor at $$A$$, draw $$\angle XAB$$ making an angle of $$\angle 60^{\circ}$$.

Step 4: Place the protractor at $$B$$, draw $$\angle YBA$$ making an angle of $$40^{\circ}$$.

Step 5: The point $$C$$ lies at the intersection of two rays $$AX$$ and $$BY$$.

Therefore, $$ABC$$ is the required triangle.