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Construct a quadrilateral PLAN if it is given PL = 4cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110° and ∠N = 85°.
Given PL =4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110° and ∠N = 85°.
To do:
Construct a quadrilateral PLAN with the given measurements.
Solution:
Steps of construction:
1. A line segment PL is drawn with length 4 cm.
2. An arc of a suitable radius is drawn cutting PL and its extended length at two points. With the same radius from P, a mark is made on this arc and another mark is made from this mark with the same radius. From these two marks, two more arcs are drawn on the same side of PL to intersect at a point. A line PX is drawn through this point. This line PX is at 90° with PL.
3. A line LY is drawn through L making an angle 75° with PL. An arc of length 6.5 cm is cut off on LY at point A.
4. A line is drawn through A making an angle of 110° with LA and cutting PX at point N.
5. PLAN is the required quadrilateral.
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