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# Practical Geometry Exercise 18.5

### Question: 1

Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.

### Solution: Steps of construction:

Step I: Draw AB = 4 cm.

Step II: Construct XA= 75° at A and AB80° at B.

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

Step IV: At C, draw BC120° such that it meets AX at D.

### Question: 2

Construct a quadrilateral ABCD, where AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B=105° and ∠D = 90°.

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

i.e. + ∠B + ∠C ∠D = 360°

105°

Steps of construction:

Step I: Draw AB = 5.5 cm.

Step II: Construct XAB=60° at A and ABY=105°.

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

Step IV: At C, draw BC105° such that it meets AX at D.

### Question: 3

Construct a quadrilateral PQRS, where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

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

i.e., ∠Q + ∠R + ∠S 360°

= 75°

Steps of construction:

Step I: Draw PQ = 3.5 cm.

Step II: Construct XP= 75° at P and PQ75° at Q.

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

Step IV: At R, draw QR105° such that it meets PX at S.

### Question: 4

Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

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

i.e. + ∠B + ∠C ∠D = 360°

95°

Steps of construction:

Step I: Draw BC = 5.5 cm.

Step II: Construct XBC=110° at A and BCY95°.

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

Step IV: At D, draw CD85° such that it meets BY at A.

### Question: 5

Construct a quadrilateral ABCD, where ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.

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

i.e. + ∠B + ∠C ∠D = 360°

= 115°

Steps of Construction:

Step I: Draw BC = 5.7 cm.

Step II: Construct XB105° at B and BC105° at C.

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

Step IV: At D, draw CD115° such that it meets BY at A.

### Question: 6

Construct a quadrilateral PQRS, in which PQ = 4 cm, QR = 5 cm, ∠P = 50°, ∠Q = 110° and ∠R = 70°.

### Solution: Steps of construction:

Step I: Draw PQ = 4 cm.

Step II: Construct XP= 50° at P and PQ110° at Q.

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

Step IV: At R, draw QR70° such that it meets PX at S.