Construct a quadrilateral ABCD where AB - 3-5 cm- BC - 6-5 cm- - A - 75- - B - 105- and - C - 120-

Step 1.Draw AB = 3.5 cm Step 2. Draw ∠ XAB = 75^∘ at A and ∠ ABY = 105^∘. Step 3. With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C. ...

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Standard VIII

Mathematics

Construction of Special Quadrilaterals

Construct a q...

Question

Construct a quadrilateral ABCD where AB = 3.5 cm, BC = 6.5 cm, $∠ A = 75^{\circ}, ∠ B = 105^{\circ}$ and $∠ C = 120^{\circ}$

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Solution

Step 1.Draw AB = 3.5 cm

Step 2. Draw $∠ X A B = 75^{\circ}$ at A and $∠ A B Y = 105^{\circ}$ .

Step 3. With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C.

Step 4. At C draw $∠ B C Z = 120^{\circ}$ such that CZ meets AX at D.

The quadrilateral ABCD so obtained is the required quadrilateral.

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Q. Construct a quadrilateral ABCD where AB = 3.5 cm, BC = 6.5 cm,

∠ A = 75^{\circ}, ∠ B = 105^{\circ}

and

∠ C = 120^{\circ}

Given below are the steps for the construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $∠ A = 75^{\circ}, ∠ B = 105^{\circ}$ and $∠ C = 120^{\circ}$ . Which of the following is wrong?
1:- Draw AB = 3.5 cm.
2:- Construct $∠ D A B = 75^{\circ}, ∠ A B C = 105^{\circ}$ at B.
3:- Draw BC = 6.5 cm.
4:- At D construct $∠ A D C = 120^{\circ}$ .

Construct a quadrilateral ABCD, where AB = 4 cm, BC = 5 cm, CD = 6.5 cm and Angle B = $105^{\circ}$ and Angle C = $80^{\circ}$ .

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Construct a quadrilateral ABCD where AB = 3.5 cm, BC = 6.5 cm, ∠A=75∘,∠B=105∘ and ∠C=120∘

Step 1.Draw AB = 3.5 cm Step 2. Draw ∠XAB=75∘ at A and ∠ABY=105∘. Step 3. With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C. Step 4. At C draw ∠BCZ=120∘ such that CZ meets AX at D. The quadrilateral ABCD so obtained is the required quadrilateral.

Construct a quadrilateral ABCD where AB = 3.5 cm, BC = 6.5 cm, $∠ A = 75^{\circ}, ∠ B = 105^{\circ}$ and $∠ C = 120^{\circ}$