Question

12. If angles A,B,C and D of the quadrilateral ABCD, taken
In orders are in the ratio 3:7:6:4, then ABCD is a
(a) parallelogram
(b)Kite
(c)rhombus
(d)trapezium​

Answer 1

Answer:

Trapezium

Step-by-step explanation:

Let the angles of quadrilateral be

3x , 7x , 6x and 4x

we know that ,

sum of all angles of a quadrilateral is 360⁰ .

Then ,

==> 3x + 7x + 6x + 4x = 360⁰

==> 20x = 360⁰

==> x = 360⁰ / 20 = 18⁰

==> x = 18⁰

Therefore ,

the angles A , B , C and D are respectively ,

∠A = 3x = 3 × 18⁰ = 54⁰

∠B = 7x = 7 × 18⁰ = 126⁰

∠C = 6x = 6 × 18⁰ = 108⁰

∠D = 4x = 4 × 18⁰ = 72⁰

Which shows that ,

∠A + ∠B = 180⁰

∠C + ∠D = 180⁰

==> AD || BC

Hence ,

ABCD is a trapezium .

Answer 2

ANSWER:

ABCD IS A TRAPEZIUM.

GIVEN:

ABCD us a quadrilateral.

Ratio of angles ABCD 3 : 7 : 6 : 4 .

TO FIND:

ABCD = ??

FORMULA:

SUM OF INTERIOR ANGLES OF A POLYGON = (n - 2)180°, where n is the number of sides.

EXPLANATION:

Quadrilateral has 4 sides => n = 4

Sum of interior angles of a quadrilateral = (4 - 2)180° = 2(180°) = 360°

From given we can write 3x + 7x + 6x + 4x = 360°

20x = 360°

x = 18°

Substitute x = 18° in 3x, 7x, 6x, 4x

3x = 3(18°) = 54°

7x = 7(18°) = 126°

6x = 6(18)° = 108°

4x = 4(18°) = 72°

$\angle A + \angle B = {180}^{ \circ} \\ \\ \angle C + \angle D = {180}^{ \circ}$

$\textbf{AD is parallel to BC}$

$\textsf{\bf{Hence the given quadrilateral is a}} \\ \textsf{\bf{trapezium}}$

NOTE: REFER ATTACHMENT FOR DIAGRAM.