 Hello and welcome to the session. Today I will help you with the following question. The question says, construct the falling quadrilateral quadrilateral PLAN where PL is 4 cm, LA is 6.5 cm, angle P is 90 degrees, angle A is 110 degrees and angle N is 85 degrees. Now before drawing the actual figure, first let's have a look at the rough sketch of the quadrilateral PLAN where PL is 4 cm, LA is 6.5 cm, angle P is 90 degrees, angle A is 110 degrees and angle N is given to be 85 degrees. Now let's move on to the solution. As you can see in the rough sketch of the quadrilateral PLAN, the three measures of the three angles are given to us but the measure of angle L is not given to us and we know that some of the angles of a quadrilateral is 360 degrees so we have angle P plus angle L plus angle A plus angle N is equal to 360 degrees. Now angle P is 90 degrees so we have 90 degrees plus angle L is not given to us so we write angle L as it is plus angle A is 110 degrees plus angle N is 85 degrees. Now this is equal to 360 degrees. This further implies that angle L plus 285 degrees is equal to 360 degrees. Which further implies that angle L is equal to 360 degrees minus 285 degrees. So we have angle L is equal to 75 degrees. Hence we have got the measure of the fourth angle as well that is angle L is 75 degrees. Now we have got all the measures of the quadrilateral PLAN so we can construct this quadrilateral step by step now. Now observing the rough sketch we can easily see that a first step of construction would be draw a line segment equal to 4 cm. So as you can see we have made a line segment PL of 4 cm. We have angle P as 90 degrees so next step would be make an angle of 90 degrees at P. So we have made an angle of 90 degrees at P. Now the measure of angle L is 75 degrees so our next step is make an angle of 75 degrees at L. So we have made an angle of 75 degrees at L. Now our next step is to locate the point A where LA is given to be 6.5 cm. So in the next step we take L as the center and radius 6.5 cm and then we draw an arc on the ray Ly. So as you can see we have made an arc of radius 6.5 cm on the ray Ly. Now let's mark this point as A where LA is 6.5 cm. Now as you can see in the rough sketch the angle is 110 degrees so our next step would be make an angle of 110 degrees at A. So we have made an angle of 110 degrees at A. Now let's mark this point of intersection of 2 rays that is Px and Az as N where angle N is 85 degrees. So as you can see we have got the required quadrilateral PLAN. Hence we have PLAN is the required quadrilateral with PL equal to 4 cm, LA equal to 6.5 cm, angle P equal to 90 degrees, angle A equal to 110 degrees and angle N as 85 degrees. Hope you enjoyed the session have a good day.