Construction of Polygons

**Construction of quadrilateral when one angle and four sides are given:**

**Example:**

Construct a quadrilateral PQRS with PQ = 6 cm, QR = 7 cm, RS = 8.5 cm, PS = 6.5 cm and ∠Q = 90°.

**Solution:**

**Step 1: **Draw line segment PQ of length 6 cm.

**Step 2: **Draw ∠XQP = 90° at point Q.

**Step 3: **Taking Q as centre and 7 cm as radius, mark an arc on QX and name the point of intersection as R.

**Step 4: **Taking R as centre and 8.5 cm as radius, mark an arc.

**Step 5: **Taking P as centre and 6.5 cm as radius, mark an arc. Let it intersect the previous arc at point S.

**Step 6:** Join PS and RS.

PQRS is the required quadrilateral.

**Construction of a quadrilateral when three sides and two included angles are given**

**Example:**

Construct a quadrilateral PQRS with SR = 6.5 cm, PS = 5 cm, QR = 3 cm, ∠R = 120°, and ∠S = 70°.

**Solution:**

The steps of construction are as follows:

**Step 1:**

Draw SR = 6.5 cm. Draw ∠SRX = 120° at R and ∠RSY = 70° at S.

**Step 2:**

With S as centre, draw an arc of radius 5 cm intersecting SY at P.

With R as cen…

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