Exercise 18.5

**1. Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, \(\angle A=75°\;\), \(\angle B=80°\;\) and \(\angle C=120°\;\).**

**Steps of construction:**

Step I: Draw AB = 4 cm.

Step II: Construct \(\angle XAB=75°\;\)

Step III: With B as the center and radius 3 cm, cut off BC = 3 cm.

Step IV: At C, draw \(\angle BCZ=120°\;\)

The quadrilateral so obtained is the required quadrilateral.

**2. Construct a quadrilateral ABCD, where AB = 5.5 cm, BC = 3.7 cm, \(\angle A=60°\;\), \(\angle B=105°\;\) and \(\angle D=90°\;\).**

We know that the sum of all the angles in a quadrilateral is 360.

i.e. \(\angle A+\angle B+\angle C+\angle D=360°\;\)

\(\angle C=105°\;\)

**Steps of construction:**

Step I: Draw AB = 5.5 cm.

Step II: Construct \(\angle XAB=60°\;\)

Step III: With B as the center and radius 3.7 cm, cut off BC = 3.7 cm

Step IV: At C, draw \(\angle BCZ=105°\;\)

The quadrilateral so obtained is the required quadrilateral.

**3. Construct a quadrilateral PQRS, where PQ = 3.5 cm, QR = 6.5 cm, \(\angle P=\angle R=105°\;\) and \(\angle S=75°\;\).**

We know that the sum of all the angles in a quadrilateral is 360.

i.e., \(\angle P+\angle Q+\angle R+\angle S=360°\;\)

\(\angle Q=75°\;\)

**Steps of construction:**

Step I: Draw PQ = 3.5 cm.

Step II: Construct \(\angle XPQ=75°\;\)

Step III: With Q as the center and radius 6.5 cm, cut off QR = 6.5

Step IV: At R, draw \(\angle QRZ=105°\;\)

The quadrilateral so obtained is the required quadrilateral.

**4. Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, \(\angle A=70°\;\), \(\angle B=110°\;\) and \(\angle D=85°\;\).**

We know that the sum of all the angles in a quadrilateral is 360. i.e.

i.e. \(\angle A+\angle B+\angle C+\angle D=360°\;\)

\(\angle C=95°\;\)

**Steps of construction:**

Step I: Draw BC = 5.5 cm.

Step II: Construct \(\angle XBC=110°\;\)

Step III: With C as the center and radius 4.1 cm, cut off CD = 4.1 cm.

Step IV: At D, draw \(\angle CDZ=85°\;\)

The quadrilateral so obtained is the required quadrilateral.

**5. Construct a quadrilateral ABCD, where \(\angle A=65°\;\), \(\angle B=105°\;\), \(\angle C=75°\;\), BC = 5.7 cm and CD = 6.8 cm.**

We know that the sum of all the angles in a quadrilateral is 360. i.e

i.e. \(\angle A+\angle B+\angle C+\angle D=360°\;\)

\(\angle D=115°\;\)

**Steps of Construction:**

Step I: Draw BC = 5.7 cm.

Step II: Construct \(\angle XBC=105°\;\)

Step III: With C as the center and radius 6.8 cm, cut off CD = 6.8 cm.

Step IV: At D, draw \(\angle CDZ=115°\;\)

The quadrilateral so obtained is the required quadrilateral.

**6. Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, \(\angle P=50°\;\), \(\angle Q=110°\;\) and \(\angle R=70°\;\).**

**Steps of construction:**

Step I: Draw PQ = 4 cm.

Step II: Construct \(\angle XPQ=50°\;\)

Step III: With Q as the center and radius 5 cm, cut off QR = 5 cm.

Step IV: At R, draw \(\angle QRZ=70°\;\)

The quadrilateral so obtained is the required quadrilateral.