Question

8. The angles of a quadrilateral are in the ratio
3 : 4 : 5 : 6. Show that the quadrilateral is a
trapezium.

Plz someone help me with this question

Answer 1

Answer:

Quadrilateral ABCD is a Trapezium.

Step-by-step explanation:

Given :

• ∠A : ∠B : ∠C : ∠D = 3 : 4 : 5 : 6

To Find :

• The Quadrilateral is a trapezium.

Solution :

Let ∠A, ∠B, ∠C and ∠D be the angles of the quadrilateral ABCD.

Since, ∠A : ∠B : ∠C : ∠D = 3 : 4 : 5 : 6

∴ ∠A = 3x

∠B = 4x

∠C = 5x

∠D = 6x

In quadrilateral ABCD,

${∠A + ∠B + ∠C + ∠D = 360° \ \ \ \ \ (ASP)} \\ \\ ∴ 3x + 4x + 5x + 6x = 360° \\ \\ \implies 18x = 360 \\ \\ \implies x = \frac{360}{18} \\ \\ \implies x = 20 \degree$

∴ Angles are 60°, 80°, 100° and 120°.

In quadrilateral ABCD,

∠A + ∠D = 60° + 120° = 180°

∠B + ∠C = 80° + 100° = 180°

∴ AB || CD (Sum of consecutive interior angles is supplementary)

But, ∠A + ∠B = 60° + 80° = 140° ≠ 180°

∴ AD is not parallel to BC.

Hence, Quadrilateral ABCD is a Trapezium.

(A quadrilateral having exactly one pair of parallel sides, is a trapezium.)

Answer 2

Answer:

It is Trapezium.

Step-by-step explanation:

Refer to the Attachment.