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# Class 8 RD Sharma Solutions – Chapter 18 Practical Geometry – Exercise 18.5

• Last Updated : 06 May, 2021

### Question 1: Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, âˆ A = 75Â°, âˆ B = 80Â° and âˆ C = 120Â°?

Solution:

We have, AB = 4 cm, BC = 3 cm, âˆ A = 75Â°, âˆ B = 80Â° and âˆ C = 120Â°.

Step 1: Draw a line segment AB = 4cm

Step 2: Construct an angle of 75Â° at A.

Step 3: Construct an angle of 80Â° at B.

Step 4: Taking B as the centre, draw an arc radius of 3 cm. Mark this point as C.

Step 5: Construct an angle of 120Â° at C such that it intersects the line segment AX. Mark that point as D.

Step 6: Now join BC, CD, and DA to form a quadrilateral.

### Question 2: Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 3.7 cm, âˆ A = 60Â°, âˆ B = 105Â° and âˆ D = 90Â°?

Solution:

We have, AB = 5.5 cm, BC = 3.7 cm, âˆ A = 60Â°, âˆ B = 105Â° and âˆ D = 90Â°.

We know that âˆ A + âˆ B + âˆ C + âˆ D = 360Â°.

âˆ´ âˆ C = 105Â°

Step 1: Draw a line segment AB = 5.5cm

Step 2: Construct an angle of 60Â° at A.

Step 3: Construct an angle of 105Â° at B.

Step 4: Taking B as the centre, draw an arc radius of 3.7 cm. Mark this point as C.

Step 5: Construct and angle of 105Â° at C such that it intersects the line segment AX. Mark that point as D.

Step 6: Now join BC, CD, and DA to form a quadrilateral.

### Question 3: Construct a quadrilateral PQRS where PQ = 3.5 cm, QR = 6.5 cm, âˆ P = âˆ R = 105Â° and âˆ S = 75Â°?

Solution:

We have, PQ = 3.5 cm, QR = 6.5 cm, âˆ P = âˆ R = 105Â° and âˆ S = 75Â°.

We know that âˆ P + âˆ Q + âˆ R + âˆ S = 360Â°

âˆ´ âˆ Q = 75Â°

Step 1: Draw a line segment PQ = 3.5cm

Step 2: Construct an angle of 105Â° at P.

Step 3: Construct an angle of 75Â° at Q.

Step 4: Taking Q as the centre, draw an arc radius of 6.5 cm. Mark this point as R.

Step 5: Construct an angle of 105Â° at R such that it intersects the line segment PX. Mark the point as S.

Step 6: Now join QR, RS, and PS to form a quadrilateral.

### Question 4: Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, âˆ A = 70Â°, âˆ B = 110Â° and âˆ D = 85Â°?

Solution:

We have, BC = 5.5 cm, CD = 4.1 cm, âˆ A = 70Â°, âˆ B = 110Â° and âˆ D = 85Â°.

We know that âˆ A + âˆ B + âˆ C + âˆ D = 360Â°

âˆ´ âˆ C = 95Â°

Step 1: Draw a line segment BC = 5.5cm

Step 2: Construct an angle of 110Â° at B.

Step 3: Construct an angle of 95Â° at C.

Step 4: Taking C as the centre, draw an arc radius of 4.1 cm. Mark this point as D.

Step 5: Construct an angle of 85Â° at D such that it intersects the line segment BX. Mark that point as A.

Step 6: Now join CD, DA, and BA to form a quadrilateral.

### Question 5: Construct a quadrilateral ABCD âˆ A = 65Â°, âˆ B = 105Â°, âˆ C = 75Â°, BC = 5.7 cm and CD = 6.8 cm?

Solution:

We have, âˆ A = 65Â°, âˆ B = 105Â°, âˆ C = 75Â°, BC = 5.7 cm and CD = 6.8 cm.

We know that âˆ A + âˆ B + âˆ C + âˆ D = 360Â°

âˆ´ âˆ D = 115Â°

Step 1: Draw a line segment BC = 5.7cm

Step 2: Construct an angle of 105Â° at B.

Step 3: Construct an angle of 75Â° at C.

Step 4: Taking C as the centre, draw an arc radius of 6.8 cm. Mark this point as D.

Step 5: Construct an angle of 115Â° at D such that it intersects the line segment BX. Mark that point as A.

Step 6: Now join CD, DA, and BA to form a quadrilateral.

### Question 6: Construct a quadrilateral PQRS in which PQ = 4 cm, QR = 5 cm âˆ P = 50Â°, âˆ Q = 110Â° and âˆ R = 70Â°?

Solution:

We have, PQ = 4 cm, QR = 5 cm âˆ P = 50Â°, âˆ Q = 110Â° and âˆ R = 70Â°.

Step 1: Draw a line segment PQ = 4cm

Step 2: Construct an angle of 50Â° at P.

Step 3: Construct an angle of 110Â° at Q.

Step 4: Taking Q as the centre, draw an arc radius of 5 cm. Mark this point as R.

Step 5: Construct an angle of 70Â° at R such that it intersects the line segment PX. Mark that point as S.

Step 6: Now join QR, RS, and PS to form a quadrilateral.

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