### Theory:

Let's see how to construct a quadrilateral when two adjacent sides and three angles are given.
Example:
Construct a quadrilateral $$CAKE$$ where $$CA = 7 \ cm$$, $$AK = 6.5 \ cm$$, $$\angle C = 90^\circ$$, $$\angle K = 110^\circ$$, $$\angle E = 100^\circ$$.

Let us first draw the rough quadrilateral, which will help us to draw a fair quadrilateral.

Rough diagram:

Fair diagram:

Step 1: Draw a line segment $$CA = 7 \ cm$$.

Step 2: Construct $$\angle ACX = 90^\circ$$ using ruler and compass.

Step 3: We know that sum of all the angles of a quadrilateral is $$360^\circ$$.

$$\angle C + \angle A + \angle K + \angle E = 360^\circ$$

$$90^\circ + \angle A + 110^\circ + 100^\circ = 360^\circ$$

So, $$\angle A = 60^\circ$$

Construct $$\angle CAY = 60^\circ$$ using ruler and compass.

Step 4: With $$A$$ as centre and $$6.5 \ cm$$ as radius, draw an arc, cutting $$AY$$ at $$K$$.

Step 5: With $$K$$ as centre, make an angle of $$110^\circ$$, cutting $$CX$$ at $$E$$, then join $$EK$$.

Thus, the quadrilateral $$CAKE$$ is obtained.