**Construct the following quadrilaterals:**

**Quadrilateral MORE**

MO = 6 cm, ∠R = 105°, OR = 4.5 cm, ∠M = 60°, ∠O = 105°

**Quadrilateral PLAN**

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

**Parallelogram HEAR**

HE = 5 cm, EA = 6 cm, ∠R = 85°

**Rectangle OKAY**

OK = 7 cm, KA = 5 cm

**Solutions:**

**1. Quadrilateral MORE**

**Given**

MO = 6 cm, ∠R = 105°, OR = 4.5 cm, ∠M = 60°, ∠O = 105°

**Steps for Construction**

**Step 1:** Draw a line ‘OR’ measuring = 4.5 cm.

**Step 2:** Draw angles of 105° from both the points ‘O’ and ‘R’, as shown below

**Step 3:** Open an arc of 6 cm then cut ‘OM’ of 6 cm, as shown in the figure below

**Step 4:** Now make an angle of 60° from point ‘M’ which will further join point ‘E’.

**Step 5:** We have the quadrilateral ‘MORE’

**2. Quadrilateral PLAN**

**Given**

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

First we will find angle L,

Sum of angles of a quadrilateral = 360°

∠P + ∠A + ∠N + ∠L = 360°

90° + 110° + 85° + ∠L = 360°

∠L = 360° – 285°

∠L = 75°

**Steps for Construction**

**Step 1:** Draw a line segment LA = 6.5 cm.

**Step 2:** Draw an angle of 75° from point L.

**Step 3: **Draw another angle of 110° from point A

**Step 4:** From point L cut PL=4 cm.

**Step 5:** From point P draw an angle of 90° which intersect the angle line extended through A at N.

Hence, we have our required quadrilateral PLAN.

**3. Parallelogram HEAR**

**Given**

HE = 5 cm, EA = 6 cm, ∠R = 85°

**Steps for Construction**

**Step 1:** Draw a line segment HE = 5 cm

**Step 2: **From point E draw an angle of 85°.

**Step 3:** From point E cut EA = 6 cm

**Step 4: **Draw an arc from center A of 5 cm, draw another arc of 6 cm with centre E, and further mark point R at the intersection of both the arcs. as shown below:

**Step 5:** Join HR and AR respectively.

Thus, we have the required quadrilateral HEAR.

**4. Rectangle OKAY**

**Given**

OK = 7 cm, KA = 5 cm

All the angles of a rectangle are 90° and the opposite sides are equal.

**Steps for Construction**

**Step 1: **Draw a line segment OK = 7 cm.

**Step 2:** Draw an 90° angle from point O.

**Step 3:** Taking point O as radius draw an arc of 5 cm as shown, and mark the point Y.

**Step 4:** Taking Points K and Y as centre draw arcs of 5 cm and 7 cm respectively, intersect both the arcs at point A.

**Step 5:** Join KA and AY.

Thus, we have the required rectangle OKAY.