##### Construct the following quadrilaterals.(i) Quadrilateral MOREMO = 6 cmOR = 4.5 cm∠M = 60°∠O = 105°∠R = 105°(ii) Quadrilateral PLANPL = 4 cmLA = 6.5 cm∠P = 90°∠A = 110°∠N = 85°(iii) Parallelogram HEARHE = 5 cmEA = 6 cm∠R = 85°

(i) The steps of construction are:

Step (a) Draw a line segment MO of 6 cm and an angle of 105° at point O.

As vertex R is 4.5 cm away from the vertex O, therefore, cut a line segment OR of 4.5 cm from this ray

Step (b) Now, draw an angle of 105° at point R

Step (c) Draw an angle of 60° at point M and this ray meet the previously drawn ray from R at point E

Thus, MORE is the required quadrilateral, as given below,

(ii) As we know that the sum of the angles of a quadrilateral is 360°

∠ P + ∠ L + ∠ A + ∠ N = 360°

90° + ∠ L + 110° + 85° = 360°

285° + ∠ L = 360°

∠ L = 360° - 285°

= 75°

The steps of construction are:

Step (a) Draw a line segment PL of 4 cm and also draw an angle of 75° at point L. Vertex A is 6.5 cm away from vertex L so cut a line segment LA of 6.5 cm from this ray

Step (b) From point A draw an angle of 110°

Step (c) Draw an angle of 90° at point P. This ray will meet the previously drawn ray from A at point N

Thus, the required quadrilateral is shown below:

(iii) The steps of construction are:

Step (a) Draw a line segment HE of 5 cm and an angle of 85° at point E.

Vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray

Step (b) Vertex R is 6 cm and 5 cm away from vertex H and A respectively.

So by taking radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will intersect each other at point R

Step (c) Join R to H and A

Thu, the required quadrilateral is shown below:

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Step (a) Draw a line segment OK of 7 cm and an angle of 90° at point K

Vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray

Step  (b) Vertex Y is of 5 cm and 7 cm away from vertex O and A respectively. Now by taking 5 cm and 7 cm as radius draw arcs from point O and A respectively and these will intersect at point Y

Step  (c) Join Y to A and O

Thus, the required quadrilateral is shown below:

1