Given below are the steps of construction of a quadrilateral ABCD- where AB - 3-5 cm- BC - 6-5 cm- - A - 75- - B - 105- and - C - 120- Which of the following options is the wrong step-1- Draw AB - 3-5 cm-2- Draw - DAB - 75- - ABC - 105- at B-3- Draw BC - 6-5 cm-4- At D draw - ADC - 120-

The wrong step is 4. Sum of all angles of a quadrilateral add upto 360^∘. ∠ A,∠ B and ∠ C add upto 300^∘. Thus the value of ∠ D should be 60^∘. But it is 120^∘ ...

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Byju's Answer

Standard VIII

Mathematics

Construction of a Quadrilateral When Two Adjacent Sides and Three Angles Are Given

Given below a...

Question

Given below are the steps of 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 options is the wrong step?
1:- Draw AB = 3.5 cm.
2:- Draw $∠ D A B = 75^{\circ}, ∠ A B C = 105^{\circ}$ at B.
3:- Draw BC = 6.5 cm.
4:- At D draw $∠ A D C = 120^{\circ}$ .

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Solution

The correct option is C 4
The wrong step is 4.
Sum of all angles of a quadrilateral add upto $360^{\circ}$ .
$∠ A$ , $∠ B$ and $∠ C$ add upto $300^{\circ}$ .
Thus the value of $∠ D$ should be $60^{\circ}$ .
But it is $120^{\circ}$ and thus does not form a quadrilateral.

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Similar questions

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

∠ A = 75^{\circ}, ∠ B = 105^{\circ}

and

∠ C = 120^{\circ}

Q. To construct a trapezium ABCD with

A B ∥ C D,

AB = 6.5 cm, BC = 6.2 cm,

∠ A B C = 80^{\circ}

and

∠ D A B = 105^{\circ},

we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle

∠ A B X = 80^{\circ}

at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

Q. To construct a trapezium ABCD with

A B ∥ C D,

AB = 6.5 cm, BC = 6.2 cm,

∠ A B C = 80^{\circ}

and

∠ D A B = 105^{\circ},

we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle

∠ A B X = 80^{\circ}

at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

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The correct option is C 4The wrong step is 4. Sum of all angles of a quadrilateral add upto 360∘. ∠A , ∠B and ∠C add upto 300∘. Thus the value of ∠D should be 60∘. But it is 120∘ and thus does not form a quadrilateral.

The correct option is C 4
The wrong step is 4.
Sum of all angles of a quadrilateral add upto $360^{\circ}$ .
$∠ A$ , $∠ B$ and $∠ C$ add upto $300^{\circ}$ .
Thus the value of $∠ D$ should be $60^{\circ}$ .
But it is $120^{\circ}$ and thus does not form a quadrilateral.