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### Theory:

• Draw a side and make an angle that is given with side measure. • Make a new angle from the newly formed side ($$X$$-axis). • Make the given angle another. This would intersect with the axis of $$Y$$ formed above. The quadrilateral is to be formed. Example:
Construct a quadrilateral $$PLAN$$ with following measurements.

$$PL = 4 cm$$, $$LA = 6.5 cm$$, $$∠P= 90°$$, $$∠A = 110°$$, $$∠N = 85°$$

The sum of the angles of a quadrilateral is $$360°$$. So, $$∠P + ∠L + ∠A + ∠N = 360°$$.

$$90° + ∠L + 110° + 85° = 360°$$

$$90° + ∠L + 195° = 360°$$

$$∠L + 285° = 360°$$

$$∠L = 360° - 285°$$

$$∠L = 75°$$

Step 1: Draw the side $$PL = 4 cm$$ and draw the angle $$75 °$$ at the point $$L$$. As the vertex $$A$$ is $$6.5 cm$$ away from $$L$$, cut the line segment $$LA$$ of $$6.5 cm$$ out from this ray. Step 2: Again, draw the angle $$110 °$$ at the point $$A$$. Step 3: Draw the angle $$90 °$$ at the point $$P$$. This ray will meet the previously drawn $$A$$ ray at the $$N$$ point. Thus, the required quadrilateral $$PLAN$$ has been constructed.