问题1：在AB = 4 cm，BC = 3 cm，∠A= 75°，∠B= 80°和∠C= 120°的情况下构造四边形ABCD?
解决方案：
We have, AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 4cm
Step 2: Construct an angle of 75° at A.
Step 3: Construct an angle of 80° 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 120° 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.
问题2：构造一个四边形ABCD，其中AB = 5.5 cm，BC = 3.7 cm，∠A= 60°，∠B= 105°，∠D= 90°?
解决方案：
We have, AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.
We know that ∠A + ∠B + ∠C + ∠D = 360°.
∴ ∠C = 105°
Steps to construct a quadrilateral:
Step 1: Draw a line segment AB = 5.5cm
Step 2: Construct an angle of 60° at A.
Step 3: Construct an angle of 105° 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 105° 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.
问题3：构造四边形PQRS，其中PQ = 3.5 cm，QR = 6.5 cm，∠P=∠R= 105°和andS = 75°?
解决方案：
We have, PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.
We know that ∠P + ∠Q + ∠R + ∠S = 360°
∴ ∠Q = 75°
Steps to construct a quadrilateral:
Step 1: Draw a line segment PQ = 3.5cm
Step 2: Construct an angle of 105° at P.
Step 3: Construct an angle of 75° 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 105° 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.
问题4：当BC = 5.5 cm，CD = 4.1 cm 、, A = 70°、, B = 110°和∠D= 85°时，构造四边形ABCD?
解决方案：
We have, BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.
We know that ∠A + ∠B + ∠C + ∠D = 360°
∴ ∠C = 95°
Steps to construct a quadrilateral:
Step 1: Draw a line segment BC = 5.5cm
Step 2: Construct an angle of 110° at B.
Step 3: Construct an angle of 95° 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 85° 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.
问题5：构建四边形ABCD∠A= 65°，∠B= 105°，∠C= 75°，BC = 5.7 cm，CD = 6.8 cm?
解决方案：
We have, ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.
We know that ∠A + ∠B + ∠C + ∠D = 360°
∴ ∠D = 115°
Steps to construct a quadrilateral:
Step 1: Draw a line segment BC = 5.7cm
Step 2: Construct an angle of 105° at B.
Step 3: Construct an angle of 75° 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 115° 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.
问题6：构造一个四边形的PQRS，其中PQ = 4 cm，QR = 5 cm∠P= 50°，∠Q= 110°，∠R= 70°?
解决方案：
We have, PQ = 4 cm, QR = 5 cm ∠P = 50°, ∠Q = 110° and ∠R = 70°.
Steps to construct a quadrilateral:
Step 1: Draw a line segment PQ = 4cm
Step 2: Construct an angle of 50° at P.
Step 3: Construct an angle of 110° 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 70° 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.
