 Hello and welcome to the session. Today I'll help you with the following question. The question says, constructive falling quadrilateral parallelogram HEAR, where HE is 5 centimeters, EA is 6 centimeters and angle R is 85 degrees. Now before drawing the actual figure, first let's see the rough sketch of the parallelogram HEAR, where HE is 5 centimeters, EA is 6 centimeters and angle R is given to be 85 degrees. Now let's move on to the solution. Now HE is equal to 5 centimeters and we know that HE is equal to AR since opposite sides of a parallelogram are equal. So we have AR is equal to 5 centimeters. Likewise we are given that EA is equal to 6 centimeters and we know that EA is equal to HR since opposite sides of a parallelogram are equal. So we have HR is equal to 6 centimeters. Now it's given that angle R is equal to 85 degrees. Angle R would be equal to angle E since opposite angles of a parallelogram are equal and hence we have that angle E is equal to 85 degrees. Now we know that some of the angles of a quadrilateral is 360 degrees. So we have angle H plus angle E plus angle A plus angle R is equal to 360 degrees. And now angle H would be equal to angle A since they are the opposite angles of a parallelogram. So angle H plus angle A can be written as 2 times angle H plus angle E is 85 degrees plus angle R is given to be 85 degrees. Now this is equal to 360 degrees. So we have 2 times angle H plus 85 plus 85 is 170 degrees is equal to 360 degrees. Now we transpose this 170 degrees to the right hand side. So we have 2 times angle H is equal to 360 degrees minus 170 degrees. Now this further implies that 2 times angle H is equal to 190 degrees. And so now to find the value for angle H we will divide both the sides by 2. So we have 2 times angle H upon 2 is equal to 190 degrees upon 2. Now this 2 and this 2 gets cancelled and we know that 95 2 times is 190 degrees. So we have angle H is equal to 95 degrees. And we know that angle H is equal to angle A since opposite angles of a parallelogram are equal. So we have angle A is also equal to 95 degrees. Now let's mark the measurements in the rough sketch. We are given H E is 5 centimeters, E A is 6 centimeters and we have found that A R is also 5 centimeters, R H is equal to 6 centimeters, angle R is 85 degrees, angle E is also 85 degrees, angle H is 95 degrees and angle A is also 95 degrees. Now visualizing the rough sketch of this parallelogram H E A R we will now construct the actual parallelogram. Now first type of construction would be draw a line segment H R equal to 6 centimeters. So we have drawn the line segment H R or R H equal to 6 centimeters. Now as we see in the rough sketch we have angle R is 85 degrees and angle H is 95 degrees. So in the next step we make angles of 85 degrees and 95 degrees at R and H respectively. So we have made angle of 85 degrees at R and an angle of 95 degrees at H. Now in the next step we locate the point E for this we will take H as the center and radius 5 centimeters and then we will cut an arc on the ray H Y. So we write with H as the center and radius 5 centimeters we cut an arc on the ray H Y. So you can see that we have cut an arc of radius 5 centimeters on this ray H Y. Now let's mark this point as E where H E is 5 centimeters. Now in the same way we will locate this point A where A R is 5 centimeters. So we write taking R as the center and radius 5 centimeters we draw an arc on the ray R X. So we have made an arc of radius 5 centimeters on the ray R X. Now let's mark this point as A. Now in the next step we join the points E and A. So joining the points E and A we get the required parallelogram H E A R where H E is given to be 5 centimeters E A is 6 centimeters and angle R is given as 85 degrees. So hope you enjoyed the session. Have a good day.